abstract = {Abstract With the aid of L{\"o}wdin's partitioning theory, an infinite series for the eigenvalue of the Schr{\"o}dinger equation is derived which does not contain energy differences in denominators. The resulting formulae are compared to those of constant denominator methods, such as perturbation theory within the Uns{\o}ld approximation and the connected moment expansion (CMX). The Uns{\o}ld formulae are easily obtained from partitioning theory by a suitable choice of the zero order Hamiltonian. Optimizing the value of the energy denominator using the first order wave function in a size-consistent way, the third order Uns{\o}ld correction vanishes, and the corresponding energy correction formula of the CMX is recovered at the second order. {\copyright} 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002},
author = {Surj{\'a}n, P{\'e}ter R. and Szabados, {\'A}gnes},
date-added = {2020-12-14 09:48:02 +0100},
date-modified = {2020-12-14 09:48:14 +0100},
doi = {https://doi.org/10.1002/qua.935},
journal = {Int. J. Quantum Chem.},
number = {1},
pages = {20-26},
title = {Constant denominator perturbative schemes and the partitioning technique},
abstract = {Abstract In computing ionization potentials via perturbative solution of the equation of motion for the ionization operator, we apply the technique of ``partitioning optimization'' elaborated recently for the calculation of correlation energy. Sample calculations indicate that second-order results may improve if the partitioning is optimized. {\copyright} 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003},
author = {Szabados, {\'A}gnes and Surj{\'a}n, P{\'e}ter R.},
date-added = {2020-12-14 09:47:13 +0100},
date-modified = {2020-12-14 09:47:27 +0100},
doi = {https://doi.org/10.1002/qua.10502},
journal = {Int. J. Quantum Chem.},
number = {2},
pages = {160-167},
title = {Optimized partitioning in PT: Application for the equation of motion describing ionization processes},
abstract = {Finite-order perturbation corrections are ambiguous since they depend on the partitioning of the Hamiltonian to a zero-order part and perturbation, and any chosen partitioning can be freely modified, e.g. by level shift projectors. To optimize low-order corrections, an approximate variational procedure is proposed to determine level shift parameters from the first-order Ansatz for the wavefunction. The resulting new partitioning scheme provides significantly better second-order results than those obtained by standard partitions like Epstein--Nesbet or M{\o}ller--Plesset. We treat the anharmonic oscillator and the atomic electron correlation energy in He, Be and Ne as numerical test cases.},
author = {A. Szabados and P.R Surjan},
date-added = {2020-12-14 09:46:14 +0100},
date-modified = {2020-12-14 09:46:34 +0100},
doi = {https://doi.org/10.1016/S0009-2614(99)00647-8},
journal = {Chem. Phys. Lett.},
number = {3},
pages = {303 - 309},
title = {Optimized partitioning in Rayleigh--Schr{\"o}dinger perturbation theory},
abstract = {Abstract We review the nature of the problem in the framework of Rayleigh--Schr{\"o}dinger perturbation theory (the polarization approximation) considering explicitly two examples: the interaction of two hydrogen atoms and the interaction of Li with H. We show, in agreement with the work of Claverie and of Morgan and Simon, that the LiH problem is dramatically different from the H2 problem. In particular, the physical states of LiH are higher in energy than an infinite number of discrete, unphysical states and they are buried in a continuum of unbound, unphysical states, which starts well below the lowest physical state. Claverie has shown that the perturbation expansion, under these circumstances, is likely to converge to an unphysical state of lower energy than the physical ground state, if it converges at all. We review, also, the application of two classes of exchange perturbation theory to LiH and larger systems. We show that the spectra of three Eisenschitz--London (EL) class, exchange perturbation theories have no continuum of unphysical states overlaying the physical states and no discrete, unphysical states below the lowest physical state. In contrast, the spectra of two Hirschfelder--Silbey class theories differ hardly at all from that found with the polarization approximation. Not one of the EL class of perturbation theories, however, eliminates all of the discrete unphysical states. The best one establishes a one-to-one correspondence between the lowest energy states of the unperturbed and perturbed Hamiltonians, and a one-to-two correspondence for the higher states. We suggest that the EL class perturbation theories would be good starting points for the development of more effective perturbation theories for intermolecular interactions.},
author = {Adams, William H.},
date-added = {2020-12-14 09:42:36 +0100},
date-modified = {2020-12-14 09:42:48 +0100},
doi = {https://doi.org/10.1002/qua.560382452},
journal = {International Journal of Quantum Chemistry},
number = {S24},
pages = {531-547},
title = {Perturbation theory of intermolecular interactions: What is the problem, are there solutions?},
author = {Daas,Timothy J. and Grossi,Juri and Vuckovic,Stefan and Musslimani,Ziad H. and Kooi,Derk P. and Seidl,Michael and Giesbertz,Klaas J. H. and Gori-Giorgi,Paola},
date-added = {2020-12-05 21:58:26 +0100},
date-modified = {2020-12-05 22:01:16 +0100},
doi = {10.1063/5.0029084},
journal = {J. Chem. Phys.},
number = {21},
pages = {214112},
title = {Large coupling-strength expansion of the M{\o}ller--Plesset adiabatic connection: From paradigmatic cases to variational expressions for the leading terms},
title = {Regularized Orbital-Optimized Second-Order M{\o}ller--Plesset Perturbation Theory: A Reliable Fifth-Order-Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers},
author = {L. W. Bertels and J. Lee and M. Head-Gordon},
doi = {10.1021/acs.jpclett.9b01641},
journal = {J. Phys. Chem. Lett.},
pages = {4170},
title = {Third-Order {M\oller--Plesset} Perturbation Theory Made Useful? Choice of Orbitals and Scaling Greatly Improves Accuracy for Thermochemistry, Kinetics, and Intermolecular Interactions},
title = {Orbital-optimized third-order {M\oller--Plesset} perturbation theory and its spin-component and spin-opposite scaled variants: Application to symmetry breaking problems},
author = {Joonho Lee and David W. Small and Martin Head-Gordon},
doi = {10.1063/1.5128795},
journal = {J. Chem. Phys.},
pages = {214103},
title = {Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states},
author = {Shepherd,James J. and Henderson,Thomas M. and Scuseria,Gustavo E.},
date-added = {2020-12-04 09:50:38 +0100},
date-modified = {2020-12-04 09:50:55 +0100},
doi = {10.1063/1.4942770},
journal = {J. Chem. Phys.},
pages = {094112},
title = {Using full configuration interaction quantum Monte Carlo in a seniority zero space to investigate the correlation energy equivalence of pair coupled cluster doubles and doubly occupied configuration interaction},
volume = {144},
year = {2016},
Bdsk-Url-1 = {https://doi.org/10.1063/1.4942770}}
@article{Henderson_2015,
author = {Henderson,Thomas M. and Bulik,Ireneusz W. and Scuseria,Gustavo E.},
date-added = {2020-12-04 09:47:58 +0100},
date-modified = {2020-12-04 09:48:17 +0100},
doi = {10.1063/1.4921986},
journal = {J. Chem. Phys.},
pages = {214116},
title = {Pair extended coupled cluster doubles},
volume = {142},
year = {2015},
Bdsk-Url-1 = {https://doi.org/10.1063/1.4921986}}
@article{Olevano_2019,
author = {Olevano,Valerio and Toulouse,Julien and Schuck,Peter},
date-added = {2020-12-04 09:46:46 +0100},
date-modified = {2020-12-04 09:46:46 +0100},
doi = {10.1063/1.5080330},
journal = {J. Chem. Phys.},
number = {8},
pages = {084112},
title = {A formally exact one-frequency-only Bethe-Salpeter-like equation. Similarities and differences between GW+BSE and self-consistent RPA},
volume = {150},
year = {2019},
Bdsk-Url-1 = {https://doi.org/10.1063/1.5080330}}
@article{Stein_2014,
author = {Stein,Tamar and Henderson,Thomas M. and Scuseria,Gustavo E.},
date-added = {2020-12-04 09:43:40 +0100},
date-modified = {2020-12-04 09:43:58 +0100},
doi = {10.1063/1.4880819},
journal = {J. Chem. Phys.},
pages = {214113},
title = {Seniority zero pair coupled cluster doubles theory},
volume = {140},
year = {2014},
Bdsk-Url-1 = {https://doi.org/10.1063/1.4880819}}
@article{Cohen_2016,
author = {Cohen, Aron J. and Mori-S\'anchez, Paula},
date-added = {2020-12-04 09:41:48 +0100},
date-modified = {2020-12-04 09:42:00 +0100},
doi = {10.1103/PhysRevA.93.042511},
journal = {Phys. Rev. A},
pages = {042511},
title = {Landscape of an exact energy functional},
abstract = {Summary This chapter contains sections titled: Introduction Formulation of the Correlation Problem Methods for Treating Electronic Correlation Recent Developments; Concluding Remarks},
author = {L\"owdin, Per-Olov},
booktitle = {Adv. Chem. Phys.},
date-added = {2020-12-04 09:13:16 +0100},
date-modified = {2020-12-04 09:16:18 +0100},
doi = {https://doi.org/10.1002/9780470143483.ch7},
pages = {207-322},
publisher = {John Wiley \& Sons, Ltd},
title = {Correlation Problem in Many-Electron Quantum Mechanics I. Review of Different Approaches and Discussion of Some Current Ideas},
abstract = { The general theory of quantum mechanics is now almost complete, the imperfections that still remain being in connection with the exact fitting in of the theory with relativity ideas. These give rise to difficulties only when high-speed particles are involved, and are therefore of no importance in the consideration of atomic and molecular structure and ordinary chemical reactions, in which it is, indeed, usually sufficiently accurate if one neglects relativity variation of mass with velocity and assumes only Coulomb forces between the various electrons and atomic nuclei. The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It there fore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation. Already before the arrival of quantum mechanics there existed a theory of atomic structure, based on Bohr's ideas of quantised orbits, which was fairly successful in a wide field. To get agreement with experiment it was found necessary to introduce the spin of the electron, giving a doubling in the number of orbits of an electron in an atom. With the help of this spin and Pauli's exclusion principle, a satisfactory theory of multiplet terms was obtained when one made the additional assumption that the electrons in an atom all set themselves with their spins parallel or antiparallel. If s denoted the magnitude of the resultant spin angular momentum, this s was combined vectorially with the resultant orbital angular momentum l to give a multiplet of multiplicity 2s + 1. The fact that one had to make this additional assumption was, however, a serious disadvantage, as no theoretical reasons to support it could be given. It seemed to show that there were large forces coupling the spin vectors of the electrons in an atom, much larger forces than could be accounted for as due to the interaction of the magnetic moments of the electrons. The position was thus that there was empirical evidence in favour of these large forces, but that their theoretical nature was quite unknown. },
author = {Dirac, Paul Adrien Maurice and Fowler, Ralph Howard},
date-added = {2020-12-03 20:45:34 +0100},
date-modified = {2020-12-03 20:48:01 +0100},
doi = {10.1098/rspa.1929.0094},
journal = {Proc. R. Soc. Lond. A},
number = {792},
pages = {714-733},
title = {Quantum mechanics of many-electron systems},
author = {Smith, J. C. and {Pribram-Jones}, A. and Burke, K.},
date-added = {2020-12-02 21:49:33 +0100},
date-modified = {2020-12-02 21:49:42 +0100},
doi = {10.1103/PhysRevB.93.245131},
journal = {Phys. Rev. B},
pages = {245131},
title = {Exact Thermal Density Functional Theory for a Model System: {{Correlation}} Components and Accuracy of the Zero-Temperature Exchange-Correlation Approximation},
abstract = {This paper discusses a family of non-linear sequence-to-sequence transformations designated as ek, ekm, {\~e}k, and ed. A brief history of the transforms is related and a simple motivation for the transforms is given. Examples are given of the application of these transformations to divergent and slowly convergent sequences. In particular the examples include numerical series, the power series of rational and meromorphic functions, and a wide variety of sequences drawn from continued fractions, integral equations, geometry, fluid mechanics, and number theory. Theorems are proven which show the effectiveness of the transformations both in accelerating the convergence of (some) slowly convergent sequences and in inducing convergence in (some) divergent sequences. The essential unity of these two motives is stressed. Theorems are proven which show that these transforms often duplicate the results of well-known, but specialized techniques. These special algorithms include Newton's iterative process, Gauss's numerical integration, an identity of Euler, the Pad{\'e} Table, and Thiele's reciprocal differences. Difficulties which sometimes arise in the use of these transforms such as irregularity, non-uniform convergence to the wrong answer, and the ambiguity of multivalued functions are investigated. The concepts of antilimit and of the spectra of sequences are introduced and discussed. The contrast between discrete and continuous spectra and the consequent contrasting response of the corresponding sequences to the e1 transformation is indicated. The characteristic behaviour of a semiconvergent (asymptotic) sequence is elucidated by an analysis of its spectrum into convergent components of large amplitude and divergent components of small amplitude.},
title = {Individual Correlations in Ensemble Density Functional Theory: State- and Density-Driven Decompositions without Additional Kohn-Sham Systems},
abstract = {Gross\textendash{}Oliveira\textendash{}Kohn density-functional theory (GOK-DFT) is an extension of DFT to excited states where the basic variable is the ensemble density, i.e. the weighted sum of ground- and excitedstate densities. The ensemble energy (i.e. the weighted sum of ground- and excited-state energies) can be obtained variationally as a functional of the ensemble density. Like in DFT, the key ingredient to model in GOK-DFT is the exchange-correlation functional. Developing density-functional approximations (DFAs) for ensembles is a complicated task as both density and weight dependencies should in principle be reproduced. In a recent paper [Phys. Rev. B 95, 035120 (2017)], the authors applied exact GOK-DFT to the simple but nontrivial Hubbard dimer in order to investigate (numerically) the importance of weight dependence in the calculation of excitation energies. In this work, we derive analytical DFAs for various density and correlation regimes by means of a Legendre\textendash{}Fenchel transform formalism. Both functional and density driven errors are evaluated for each DFA. Interestingly, when the ensemble exact-exchange-only functional is used, these errors can be large, in particular if the dimer is symmetric, but they cancel each other so that the excitation energies obtained by linear interpolation are always accurate, even in the strongly correlated regime.},
author = {Deur, Killian and Mazouin, Laurent and Senjean, Bruno and Fromager, Emmanuel},
title = {Exact Ensemble Density Functional Theory for Excited States in a Model System: {{Investigating}} the Weight Dependence of the Correlation Energy},
abstract = {Abstract We review coupled cluster (CC) theory for electronically excited states. We outline the basics of a CC response theory framework that allows the transfer of the attractive accuracy and convergence properties associated with CC methods over to the calculation of electronic excitation energies and properties. Key factors affecting the accuracy of CC excitation energy calculations are discussed as are some of the key CC models in this field. To aid both the practitioner as well as the developer of CC excited state methods, we also briefly discuss the key computational steps in a working CC response implementation. Approaches aimed at extending the application range of CC excited state methods either in terms of molecular size and phenomena or in terms of environment (solution and proteins) are also discussed. {\copyright} 2011 John Wiley \& Sons, Ltd. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods},
author = {Sneskov, Kristian and Christiansen, Ove},
title = {Spin-Flip Equation-of-Motion Coupled-Cluster Electronic Structure Method for a Description of Excited States, Bond Breaking, Diradicals, and Triradicals},
volume = {39},
year = {2006},
Bdsk-Url-1 = {https://doi.org/10.1021/ar0402006}}
@article{Dreuw_2005,
author = {Dreuw, Andreas and Head-Gordon, Martin},
title = {Hyperspherical harmonics: applications in quantum theory},
year = {1989}}
@book{CramerBook,
author = {C. J. Cramer},
date-added = {2020-12-01 21:06:44 +0100},
date-modified = {2020-12-01 21:06:44 +0100},
keywords = {qmech},
publisher = {Wiley},
title = {Essentials of Computational Chemistry: Theories and Models},
year = {2004}}
@book{FetterBook,
author = {A. L. Fetter and J. D. Waleck},
date-added = {2020-12-01 21:06:44 +0100},
date-modified = {2020-12-01 21:06:44 +0100},
publisher = {McGraw Hill, San Francisco},
title = {Quantum Theory of Many Particle Systems},
year = {1971}}
@book{HerzbergBook,
author = {K. P. Huber and G. Herzberg},
date-added = {2020-12-01 21:06:44 +0100},
date-modified = {2020-12-01 21:06:44 +0100},
publisher = {van Nostrand Reinhold Company},
title = {Molecular Spectra and Molecular Structure: IV. Constants of diatomic molecules},
year = {1979}}
@book{JensenBook,
address = {New York},
author = {F. Jensen},
date-added = {2020-12-01 21:06:44 +0100},
date-modified = {2020-12-01 21:06:44 +0100},
edition = {3rd},
keywords = {qmech},
publisher = {Wiley},
title = {Introduction to Computational Chemistry},
year = {2017}}
@book{NISTbook,
address = {New York},
date-added = {2020-12-01 21:06:44 +0100},
date-modified = {2020-12-01 21:06:44 +0100},
editor = {F. W. J. Olver and D. W. Lozier and R. F. Boisvert and C. W. Clark},
keywords = {maths},
publisher = {Cambridge University Press},
title = {NIST Handbook of Mathematical Functions},
year = {2010}}
@book{ParrBook,
address = {Clarendon Press},
author = {R. G. Parr and W. Yang},
date-added = {2020-12-01 21:06:44 +0100},
date-modified = {2020-12-01 21:06:44 +0100},
keywords = {dft; qmech},
publisher = {Oxford},
title = {Density-Functional Theory of Atoms and Molecules},
year = {1989}}
@book{ReiningBook,
author = {Martin, R.M. and Reining, L. and Ceperley, D.M.},
date-added = {2020-12-01 21:06:44 +0100},
date-modified = {2020-12-01 21:06:44 +0100},
isbn = {0521871506},
publisher = {Cambridge University Press},
title = {Interacting Electrons: Theory and Computational Approaches},
year = {2016}}
@book{Schuck_Book,
author = {P. Ring and P. Schuck},
date-added = {2020-12-01 21:06:44 +0100},
date-modified = {2020-12-01 21:06:44 +0100},
publisher = {Springer},
title = {The Nuclear Many-Body Problem},
year = {2004}}
@book{Stefanucci_2013,
abstract = {"The Green's function method is one of the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. This book provides a unique, self-contained introduction to nonequilibrium many-body theory. Starting with basic quantum mechanics, the authors introduce the equilibrium and nonequilibrium Green's function formalisms within a unified framework called the contour formalism. The physical content of the contour Green's functions and the diagrammatic expansions are explained with a focus on the time-dependent aspect. Every result is derived step-by-step, critically discussed and then applied to different physical systems, ranging from molecules and nanostructures to metals and insulators. With an abundance of illustrative examples, this accessible book is ideal for graduate students and researchers who are interested in excited state properties of matter and nonequilibrium physics"--},
address = {Cambridge},
author = {Stefanucci, Gianluca and van Leeuwen, Robert},
abstract = {Finite size scaling for calculations of the critical parameters of the few-body Schr{\"o}dinger equation is based on taking the number of elements in a complete basis set as the size of the system. We show in an analogy with Yang and Lee theorem, which states that singularities of the free energy at phase transitions occur only in the thermodynamic limit, that singularities in the ground state energy occur only in the infinite complete basis set limit. To illustrate this analogy in the complex-parameter space, we present calculations for Yukawa type potential, and a Coulomb type potential for two-electron atoms.},
author = {Sabre Kais and Craig Wenger and Qi Wei},
date-added = {2020-11-27 20:54:34 +0100},
date-modified = {2020-11-27 20:55:08 +0100},
doi = {https://doi.org/10.1016/j.cplett.2006.03.035},
journal = {Chem. Phys. Lett.},
pages = {45 - 49},
title = {Quantum criticality at the infinite complete basis set limit: A thermodynamic analog of the Yang and Lee theorem},
abstract = {The Schr{\"o}dinger equation for an atom or molecule includes parameters, such as bond lengths or nuclear charges, and the resulting energy eigenvalue can be treated as a function with the parameter values as continuous variables. Analysis of singular points of this function, at nonphysical parameter values, can explain and predict the success or failure of quantum chemical calculation methods. An introduction to the theory of singularities in functions of a complex variable is presented and examples of applications to quantum chemistry are described, including the calculation of molecular potential energy curves, the theoretical description of ionization, and the summation of perturbation theories.},
author = {David Z. Goodson},
booktitle = {Mathematical Physics in Theoretical Chemistry},
date-added = {2020-11-25 09:13:38 +0100},
date-modified = {2020-11-25 09:14:27 +0100},
doi = {https://doi.org/10.1016/B978-0-12-813651-5.00009-7},
editor = {S.M. Blinder and J.E. House},
isbn = {978-0-12-813651-5},
keywords = {Singularities, Avoided crossings, Quadratic approximants, Molecular potential energy curves, Ionization, Finite-size scaling, Perturbation theory, Series summation},
pages = {295 - 325},
publisher = {Elsevier},
series = {Developments in Physical {\&} Theoretical Chemistry},
title = {Chapter 9 - Singularity analysis in quantum chemistry},
abstract = {The quadratic Pade method-a new method for calculating the local density of states in various physical systems-is introduced and discussed. The method is based upon the use of Hermite-Pade polynomials and it makes the calculation of densities of states a straightforward and relatively simple matter. Its advantages over other methods with similar generality and complexity are outlined and numerical results for various systems, which illustrate the virtues of the new method, are presented and discussed.},
author = {I L Mayer and B Y Tong},
date-added = {2020-11-25 09:01:38 +0100},
date-modified = {2020-11-25 09:03:36 +0100},
doi = {10.1088/0022-3719/18/17/008},
journal = {J. Phys. C.: Solid State Phys.},
pages = {3297--3318},
title = {The quadratic Pade approximant method and its application for calculating densities of states},
author = {R. H. Nobes and J. A. Pople and L. Radom and N. C. Handy and P. J. Knowles},
doi = {10.1016/0009-2614(87)80545-6},
journal = {Chem. Phys. Lett.},
pages = {481},
title = {Slow convergence of the {M\oller--Plesset} perturbation series: the dissociation energy of hydrogen cyanide and the electron affinity of the cyano radical},
abstract = { An analysis of the `linear combination of atomic orbitals' approximation using the accurate molecular orbital equations shows that it does not lead to equations of the form usually assumed in the semi-empirical molecular orbital method. A new semi-empirical method is proposed, therefore, in terms of equivalent orbitals. The equations obtained, which do have the usual form, are applicable to a large class of molecules and do not involve the approximations that were thought necessary. In this method the ionization potentials are calculated by treating certain integrals as semi-empirical parameters. The value of these parameters is discussed in terms of the localization of equivalent orbitals and some approximate rules are suggested. As an illustration the ionization potentials of the paraffin series are considered and good agreement between the observed and calculated values is found. },
author = {Hall, G. G. and Lennard-Jones, John Edward},
date-added = {2020-11-24 09:45:15 +0100},
date-modified = {2020-11-24 09:45:50 +0100},
doi = {10.1098/rspa.1951.0048},
journal = {Proc. R. Soc. Lond. A},
pages = {541-552},
title = {The molecular orbital theory of chemical valency VIII. A method of calculating ionization potentials},
author = {Pavel Cejnar and Pavel Str{\'a}nsk{\'y} and Michal Macek and Michal Kloc},
date-added = {2020-11-20 09:33:29 +0100},
date-modified = {2020-11-20 09:33:35 +0100},
eprint = {2011.01662},
primaryclass = {quant-ph},
title = {Excited-state quantum phase transitions},
year = {2020}}
@book{GilmoreBook,
author = {Gilmore, R.},
date-added = {2020-11-20 09:31:27 +0100},
date-modified = {2020-11-20 09:31:51 +0100},
publisher = {New York, Wiley},
title = {Catastrophe Theory for Scientists and Engineers},
year = {1981}}
@book{SachdevBook,
author = {Sachdev, S.},
date-added = {2020-11-20 09:30:52 +0100},
date-modified = {2020-11-20 09:31:18 +0100},
publisher = {Cambridge University Press},
title = {Quantum Phase Transitions},
year = {1999}}
@article{Vojta_2003,
abstract = {In recent years, quantum phase transitions have attracted the interest of both theorists and experimentalists in condensed matter physics. These transitions, which are accessed at zero temperature by variation of a non-thermal control parameter, can influence the behaviour of electronic systems over a wide range of the phase diagram. Quantum phase transitions occur as a result of competing ground state phases. The cuprate superconductors which can be tuned from a Mott insulating to a d-wave superconducting phase by carrier doping are a paradigmatic example. This review introduces important concepts of phase transitions and discusses the interplay of quantum and classical fluctuations near criticality. The main part of the article is devoted to bulk quantum phase transitions in condensed matter systems. Several classes of transitions will be briefly reviewed, pointing out, e.g., conceptual differences between ordering transitions in metallic and insulating systems. An interesting separate class of transitions is boundary phase transitions where only degrees of freedom of a subsystem become critical; this will be illustrated in a few examples. The article is aimed at bridging the gap between high-level theoretical presentations and research papers specialized in certain classes of materials. It will give an overview on a variety of different quantum transitions, critically discuss open theoretical questions, and frequently make contact with recent experiments in condensed matter physics.},
title = {Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction},
abstract = {A study is made of the general Hartree---Fock (GHF) method, in which the basic spin-orbitals may be mixtures of functions having α and β spins. The existence of the solutions to the GHF equations has been proven by Lieb and Simon, and the nature of the various types of solutions has been group theoretically classified by Fukutome. Some numerical applications using Gaussian bases are carried out for some simple systems: the beryllium and carbon atoms and the BH molecule. Some GHF solutions of the general Fukutome-type ``torsional spin density waves'' (TSDW) were found.},
author = {Istv{\'a}n Mayer and Per-Olov L{\"o}wdin},
date-added = {2020-11-19 09:09:18 +0100},
date-modified = {2020-11-19 09:09:26 +0100},
doi = {https://doi.org/10.1016/0009-2614(93)85341-K},
issn = {0009-2614},
journal = {Chemical Physics Letters},
number = {1},
pages = {1 - 6},
title = {Some comments on the general Hartree---Fock method},
author = {A. T. B. Gilbert and N. A. Besley and P. M. W. Gill},
date-added = {2020-11-18 21:16:52 +0100},
date-modified = {2020-11-18 21:16:52 +0100},
doi = {10.1021/jp801738f},
journal = {J. Phys. Chem. A},
pages = {13164},
title = {Self-Consistent Field Calculations of Excited States Using the Maximum Overlap Method {(MOM)}},
volume = {112},
year = {2008},
Bdsk-Url-1 = {https://doi.org/10.1021/jp801738f}}
@article{Burton_2018,
abstract = {We explore the existence and behavior of holomorphic restricted Hartree-Fock (h-RHF) solutions for two-electron problems. Through algebraic geometry, the exact number of solutions with n basis functions is rigorously identified as 1/2(3n - 1), proving that states must exist for all molecular geometries. A detailed study on the h-RHF states of HZ (STO3G) then demonstrates both the conservation of holomorphic solutions as geometry or atomic charges are varied and the emergence of complex h-RHF solutions at coalescence points. Using catastrophe theory, the nature of these coalescence points is described, highlighting the influence of molecular symmetry. The h-RHF states of HHeH2+ and HHeH (STO-3G) are then compared, illustrating the isomorphism between systems with two electrons and two electron holes. Finally, we explore the h-RHF states of ethene (STO-3G) by considering the $\pi$ electrons as a two-electron problem and employ NOCI to identify a crossing of the lowest energy singlet and triplet states at the perpendicular geometry.},
author = {Burton, Hugh G. A. and Gross, Mark and Thom, Alex J. W.},
date-added = {2020-11-18 21:16:36 +0100},
date-modified = {2020-11-18 21:16:36 +0100},
doi = {10.1021/acs.jctc.7b00980},
file = {/Users/loos/Zotero/storage/E9FNMAU8/Burton et al. - 2018 - Holomorphic Hartree--Fock Theory The Nature of Two.pdf},
abstract = {This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy\textendash{}Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the `failure' of the Kohn\textendash{}Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree\textendash{}Fock and Bethe ansatz local density approximation) to show their successes and limitations. We also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for density functional energy components, several limits of the exact functional (weak- and strong-coupling, symmetric and asymmetric), various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H2.},
author = {Carrascal, D J and Ferrer, J and Smith, J C and Burke, K},
date-added = {2020-11-14 21:44:15 +0100},
date-modified = {2020-11-14 21:44:15 +0100},
doi = {10.1088/0953-8984/27/39/393001},
file = {/Users/loos/Zotero/storage/LRMWNYEQ/Carrascal et al. - 2015 - The Hubbard dimer a density functional case study.pdf},
issn = {0953-8984, 1361-648X},
journal = {J. Phys. Condens. Matter},
language = {en},
month = oct,
number = {39},
pages = {393001},
shorttitle = {The {{Hubbard}} Dimer},
title = {The {{Hubbard}} Dimer: A Density Functional Case Study of a Many-Body Problem},
abstract = {The asymmetric Hubbard dimer is used to study the density-dependence of the exact frequencydependent kernel of linear-response time-dependent density functional theory. The exact form of the kernel is given, and the limitations of the adiabatic approximation utilizing the exact ground-state functional are shown. The oscillator strength sum rule is proven for lattice Hamiltonians, and relative oscillator strengths are defined appropriately. The method of Casida for extracting oscillator strengths from a frequencydependent kernel is demonstrated to yield the exact result with this kernel. An unambiguous way of labelling the nature of excitations is given. The fluctuation-dissipation theorem is proven for the groundstate exchange-correlation energy. The distinction between weak and strong correlation is shown to depend on the ratio of interaction to asymmetry. A simple interpolation between carefully defined weak-correlation and strong-correlation regimes yields a density-functional approximation for the kernel that gives accurate transition frequencies for both the single and double excitations, including charge-transfer excitations. Many exact results, limits, and expansions about those limits are given in the Appendices.},
author = {Carrascal, Diego J. and Ferrer, Jaime and Maitra, Neepa and Burke, Kieron},
date-added = {2020-11-14 21:44:15 +0100},
date-modified = {2020-11-14 21:44:15 +0100},
doi = {10.1140/epjb/e2018-90114-9},
journal = {Eur. Phys. J. B},
pages = {142},
title = {Linear Response Time-Dependent Density Functional Theory of the {{Hubbard}} Dimer},
abstract = { A systematic method is developed for estimating or calculating corrections for configuration interaction in atomic, molecular and nuclear wave-function calculations. Solutions of the Hartree-Fock equations for a single Slater determinant or approximate Hartree-Fock solutions obtained by Roothaan's iterative procedure have special properties which are used to simplify the matrix of the many-particle Hamiltonian. A restricted self-consistent field method is proposed for treating states of low symmetry. This method avoids the off-diagonal Lagrange multipliers encountered in previous methods and is adapted to configuration interaction calculations. },
author = {Nesbet, R. K. and Hartree, Douglas Rayner},
date-added = {2020-11-12 10:01:40 +0100},
date-modified = {2020-11-12 10:02:40 +0100},
doi = {10.1098/rspa.1955.0134},
journal = {Proc. R. Soc. Lond. A},
number = {1182},
pages = {312-321},
title = {Configuration interaction in orbital theories},
abstract = {For non-Hermitian Hamiltonians with an isolated degeneracy (`exceptional point'), a model for cycling around loops that enclose or exclude the degeneracy is solved exactly in terms of Bessel functions. Floquet solutions, returning exactly to their initial states (up to a constant) are found, as well as exact expressions for the adiabatic multipliers when the evolving states are represented as a superposition of eigenstates of the instantaneous Hamiltonian. Adiabatically (i.e. for slow cycles), the multipliers of exponentially subdominant eigenstates can vary wildly, unlike those driven by Hermitian operators, which change little. These variations are explained as an example of the Stokes phenomenon of asymptotics. Improved (superadiabatic) approximations tame the variations of the multipliers but do not eliminate them.},
author = {M V Berry and R Uzdin},
date-added = {2020-11-12 09:14:42 +0100},
date-modified = {2020-11-12 09:20:26 +0100},
doi = {10.1088/1751-8113/44/43/435303},
journal = {J. Phys. A Math. Theor.},
month = {oct},
number = {43},
pages = {435303},
publisher = {{IOP} Publishing},
title = {Slow non-Hermitian cycling: exact solutions and the Stokes phenomenon},
author = {Doppler, J\"org and Mailybaev, Alexei A. and B\"ohm, Julian and Kuhl, Ulrich and Girschik, Adrian and Libisch, Florian and Milburn, Thomas J. and Rabl, Peter and Moiseyev, Nimrod and Rotter, Stefan},
date-added = {2019-01-20 22:03:11 +0100},
date-modified = {2019-01-20 22:03:11 +0100},
doi = {10.1038/nature18605},
journal = {Nature},
month = sep,
number = {7618},
pages = {76-79},
title = {{Dynamically Encircling an Exceptional Point for Asymmetric Mode Switching}},
author = {Guo, A. and Salamo, G. J. and Duchesne, D. and Morandotti, R. and {Volatier-Ravat}, M. and Aimez, V. and Siviloglou, G. A. and Christodoulides, D. N.},
date-added = {2019-01-20 22:03:11 +0100},
date-modified = {2019-01-21 16:26:27 +0100},
doi = {10.1103/PhysRevLett.103.093902},
journal = {Phys. Rev. Lett.},
month = aug,
number = {9},
pages = {093902},
title = {Observation of {PT Symmetry Breaking in Complex Optical Potentials}},
author = {Peng, Bo and \"Ozdemir, {\c S}ahin Kaya and Lei, Fuchuan and Monifi, Faraz and Gianfreda, Mariagiovanna and Long, Gui Lu and Fan, Shanhui and Nori, Franco and Bender, Carl M. and Yang, Lan},
date-added = {2019-01-20 22:03:11 +0100},
date-modified = {2019-01-20 22:03:11 +0100},
doi = {10.1038/nphys2927},
journal = {Nat. Phys.},
month = may,
number = {5},
pages = {394-398},
title = {{Parity\textendash{}Time-Symmetric Whispering-Gallery Microcavities}},
author = {Regensburger, Alois and Bersch, Christoph and Miri, Mohammad-Ali and Onishchukov, Georgy and Christodoulides, Demetrios N. and Peschel, Ulf},
date-added = {2019-01-20 22:03:11 +0100},
date-modified = {2019-01-20 22:03:11 +0100},
doi = {10.1038/nature11298},
journal = {Nature},
month = aug,
number = {7410},
pages = {167-171},
title = {{Parity\textendash{}Time Synthetic Photonic Lattices}},
author = {R\"uter, Christian E. and Makris, Konstantinos G. and {El-Ganainy}, Ramy and Christodoulides, Demetrios N. and Segev, Mordechai and Kip, Detlef},
date-added = {2019-01-20 22:03:11 +0100},
date-modified = {2019-01-20 22:03:11 +0100},
doi = {10.1038/nphys1515},
journal = {Nat. Phys.},
month = mar,
number = {3},
pages = {192-195},
title = {{Observation of Parity\textendash{}Time Symmetry in Optics}},
author = {El-Ganainy, Ramy and Makris, Konstantinos G. and Khajavikhan, Mercedeh and Musslimani, Ziad H. and Rotter, Stefan and Christodoulides, Demetrios N.},
date-added = {2019-01-30 12:10:10 +0100},
date-modified = {2019-01-30 12:10:10 +0100},
doi = {10.1038/nphys4323},
journal = {Nat. Phys.},
language = {en},
month = jan,
number = {1},
pages = {11-19},
title = {{Non-Hermitian Physics and PT Symmetry}},
