2028 lines
72 KiB
BibTeX
2028 lines
72 KiB
BibTeX
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@article{Ceperley_1983,
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abstract = {Random walks with branching have been used to calculate exact properties of the ground state of quantum many-body systems. In this paper, a more general Green's function identity is derived which relates the potential energy, a trial wavefunction, and a trial density matrix to the rules of a branched random walk. It is shown that an efficient algorithm requires a good trial wavefunction, a good trial density matrix, and a good sampling of this density matrix. An accurate density matrix is constructed for Coulomb systems using the path integral formula. The random walks from this new algorithm diffuse through phase space an order of magnitude faster than the previous Green's Function Monte Carlo method. In contrast to the simple diffusion Monte Carlo algorithm, it is an exact method. Representative results are presented for several molecules.},
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author = {D Ceperley},
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date-modified = {2022-10-05 14:41:32 +0200},
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||
doi = {https://doi.org/10.1016/0021-9991(83)90161-4},
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||
issn = {0021-9991},
|
||
journal = {J. Comput. Phys.},
|
||
number = {3},
|
||
pages = {404-422},
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||
title = {The simulation of quantum systems with random walks: A new algorithm for charged systems},
|
||
url = {https://www.sciencedirect.com/science/article/pii/0021999183901614},
|
||
volume = {51},
|
||
year = {1983},
|
||
bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/0021999183901614},
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||
bdsk-url-2 = {https://doi.org/10.1016/0021-9991(83)90161-4}}
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||
|
||
@article{Kalos_1962,
|
||
author = {Kalos, M. H.},
|
||
doi = {10.1103/PhysRev.128.1791},
|
||
issue = {4},
|
||
journal = {Phys. Rev.},
|
||
month = {Nov},
|
||
numpages = {0},
|
||
pages = {1791--1795},
|
||
publisher = {American Physical Society},
|
||
title = {Monte Carlo Calculations of the Ground State of Three- and Four-Body Nuclei},
|
||
url = {https://link.aps.org/doi/10.1103/PhysRev.128.1791},
|
||
volume = {128},
|
||
year = {1962},
|
||
bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRev.128.1791},
|
||
bdsk-url-2 = {https://doi.org/10.1103/PhysRev.128.1791}}
|
||
|
||
@article{Kalos_1970,
|
||
author = {Kalos, M. H.},
|
||
doi = {10.1103/PhysRevA.2.250},
|
||
issue = {1},
|
||
journal = {Phys. Rev. A},
|
||
month = {Jul},
|
||
numpages = {0},
|
||
pages = {250--255},
|
||
publisher = {American Physical Society},
|
||
title = {Energy of a Boson Fluid with Lennard-Jones Potentials},
|
||
url = {https://link.aps.org/doi/10.1103/PhysRevA.2.250},
|
||
volume = {2},
|
||
year = {1970},
|
||
bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.2.250},
|
||
bdsk-url-2 = {https://doi.org/10.1103/PhysRevA.2.250}}
|
||
|
||
@article{Moskowitz_1986,
|
||
author = {Moskowitz,Jules W. and Schmidt,K. E.},
|
||
date-modified = {2022-10-05 14:41:57 +0200},
|
||
doi = {10.1063/1.451046},
|
||
journal = {J. Chem. Phys.},
|
||
number = {5},
|
||
pages = {2868-2874},
|
||
title = {The domain Green's function method},
|
||
volume = {85},
|
||
year = {1986},
|
||
bdsk-url-1 = {https://doi.org/10.1063/1.451046}}
|
||
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||
@misc{note,
|
||
note = {As $\tau \rightarrow 0$ and $N \rightarrow \infty$ with $N\tau=t$, the operator $T^N$ converges to $e^{-t(H-E \Id)}$. We then have $G^E_{ij} \rightarrow \int_0^{\infty} dt \mel{i}{e^{-t(H-E \Id)}}{j}$, which is the Laplace transform of the time-dependent Green's function $\mel{i}{e^{-t(H-E \Id)}}{j}$.}}
|
||
|
||
@article{Willow_2012,
|
||
author = {Willow,Soohaeng Yoo and Kim,Kwang S. and Hirata,So},
|
||
date-modified = {2022-09-30 16:10:46 +0200},
|
||
doi = {10.1063/1.4768697},
|
||
journal = {J. Chem. Phys.},
|
||
number = {20},
|
||
pages = {204122},
|
||
title = {Stochastic evaluation of second-order many-body perturbation energies},
|
||
volume = {137},
|
||
year = {2012},
|
||
bdsk-url-1 = {https://doi.org/10.1063/1.4768697}}
|
||
|
||
@article{Petruzielo_2012,
|
||
author = {Petruzielo, F. R. and Holmes, A. A. and Changlani, Hitesh J. and Nightingale, M. P. and Umrigar, C. J.},
|
||
date-modified = {2022-09-30 16:12:05 +0200},
|
||
doi = {10.1103/PhysRevLett.109.230201},
|
||
issue = {23},
|
||
journal = {Phys. Rev. Lett.},
|
||
month = {Dec},
|
||
numpages = {5},
|
||
pages = {230201},
|
||
publisher = {American Physical Society},
|
||
title = {Semistochastic Projector Monte Carlo Method},
|
||
url = {https://link.aps.org/doi/10.1103/PhysRevLett.109.230201},
|
||
volume = {109},
|
||
year = {2012},
|
||
bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.109.230201},
|
||
bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.109.230201}}
|
||
|
||
@article{Caffarel_2019,
|
||
author = {Caffarel,Michel},
|
||
date-modified = {2022-09-30 16:11:35 +0200},
|
||
doi = {10.1063/1.5114703},
|
||
journal = {J. Chem. Phys.},
|
||
number = {6},
|
||
pages = {064101},
|
||
title = {Evaluating two-electron-repulsion integrals over arbitrary orbitals using zero variance Monte Carlo: Application to full configuration interaction calculations with Slater-type orbitals},
|
||
volume = {151},
|
||
year = {2019},
|
||
bdsk-url-1 = {https://doi.org/10.1063/1.5114703}}
|
||
|
||
@article{Zhang_2003,
|
||
author = {Zhang, Shiwei and Krakauer, Henry},
|
||
doi = {10.1103/PhysRevLett.90.136401},
|
||
issue = {13},
|
||
journal = {Phys. Rev. Lett.},
|
||
month = {Apr},
|
||
numpages = {4},
|
||
pages = {136401},
|
||
publisher = {American Physical Society},
|
||
title = {Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants},
|
||
url = {https://link.aps.org/doi/10.1103/PhysRevLett.90.136401},
|
||
volume = {90},
|
||
year = {2003},
|
||
bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.90.136401},
|
||
bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.90.136401}}
|
||
|
||
@article{Cleland_2010,
|
||
author = {Cleland,Deidre and Booth,George H. and Alavi,Ali},
|
||
date-modified = {2022-09-15 10:21:21 +0200},
|
||
doi = {10.1063/1.3302277},
|
||
journal = {J. Chem. Phys.},
|
||
number = {4},
|
||
pages = {041103},
|
||
title = {Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo},
|
||
volume = {132},
|
||
year = {2010},
|
||
bdsk-url-1 = {https://doi.org/10.1063/1.3302277}}
|
||
|
||
@article{Chan_2011,
|
||
abstract = { The density matrix renormalization group is a method that is useful for describing molecules that have strongly correlated electrons. Here we provide a pedagogical overview of the basic challenges of strong correlation, how the density matrix renormalization group works, a survey of its existing applications to molecular problems, and some thoughts on the future of the method. },
|
||
author = {Chan, Garnet Kin-Lic and Sharma, Sandeep},
|
||
date-modified = {2022-09-15 10:22:30 +0200},
|
||
doi = {10.1146/annurev-physchem-032210-103338},
|
||
journal = {Annu. Rev. Phys. Chem.},
|
||
number = {1},
|
||
pages = {465-481},
|
||
title = {The Density Matrix Renormalization Group in Quantum Chemistry},
|
||
volume = {62},
|
||
year = {2011},
|
||
bdsk-url-1 = {https://doi.org/10.1146/annurev-physchem-032210-103338}}
|
||
|
||
@article{White_1999,
|
||
author = {White,Steven R. and Martin,Richard L.},
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||
date-modified = {2022-09-15 10:21:52 +0200},
|
||
doi = {10.1063/1.478295},
|
||
journal = {J. Chem. Phys.},
|
||
number = {9},
|
||
pages = {4127-4130},
|
||
title = {Ab initio quantum chemistry using the density matrix renormalization group},
|
||
volume = {110},
|
||
year = {1999},
|
||
bdsk-url-1 = {https://doi.org/10.1063/1.478295}}
|
||
|
||
@article{Booth_2009,
|
||
author = {Booth,George H. and Thom,Alex J. W. and Alavi,Ali},
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||
date-modified = {2022-09-15 10:21:12 +0200},
|
||
doi = {10.1063/1.3193710},
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||
journal = {J. Chem. Phys.},
|
||
number = {5},
|
||
pages = {054106},
|
||
title = {Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space},
|
||
volume = {131},
|
||
year = {2009},
|
||
bdsk-url-1 = {https://aip.scitation.org/doi/abs/10.1063/1.3193710},
|
||
bdsk-url-2 = {https://doi.org/10.1063/1.3193710}}
|
||
|
||
@article{Tubman_2020,
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||
author = {Tubman, Norm M. and Freeman, C. Daniel and Levine, Daniel S. and Hait, Diptarka and Head-Gordon, Martin and Whaley, K. Birgitta},
|
||
date-modified = {2022-09-15 10:20:56 +0200},
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||
doi = {10.1021/acs.jctc.8b00536},
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||
journal = {J. Chem. Theory Comput.},
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||
number = {4},
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||
pages = {2139-2159},
|
||
title = {Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method},
|
||
volume = {16},
|
||
year = {2020},
|
||
bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.8b00536}}
|
||
|
||
@article{Schriber_2016,
|
||
author = {Schriber,Jeffrey B. and Evangelista,Francesco A.},
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||
date-modified = {2022-09-15 10:20:28 +0200},
|
||
doi = {10.1063/1.4948308},
|
||
journal = {J. Chem. Phys.},
|
||
number = {16},
|
||
pages = {161106},
|
||
title = {Communication: An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy},
|
||
volume = {144},
|
||
year = {2016},
|
||
bdsk-url-1 = {https://doi.org/10.1063/1.4948308}}
|
||
|
||
@article{Holmes_2016,
|
||
author = {Holmes, Adam A. and Tubman, Norm M. and Umrigar, C. J.},
|
||
date-modified = {2022-09-15 10:20:10 +0200},
|
||
doi = {10.1021/acs.jctc.6b00407},
|
||
journal = {J. Chem. Theory Comput.},
|
||
number = {8},
|
||
pages = {3674-3680},
|
||
title = {Heat-Bath Configuration Interaction: An Efficient Selected Configuration Interaction Algorithm Inspired by Heat-Bath Sampling},
|
||
volume = {12},
|
||
year = {2016},
|
||
bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.6b00407}}
|
||
|
||
@article{Harrison_1991,
|
||
author = {Robert J. Harrison},
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||
date-modified = {2022-09-15 10:18:39 +0200},
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||
doi = {10.1063/1.460537},
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||
journal = {J. Chem. Phys.},
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pages = {5021-5031},
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||
title = {Approximating full configuration interaction with selected configuration interaction and perturbation theory},
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volume = {94},
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year = {1991},
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bdsk-url-1 = {https://doi.org/10.1063/1.460537}}
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@article{Gutzwiller_1963,
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author = {Gutzwiller, Martin C.},
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||
doi = {10.1103/PhysRevLett.10.159},
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||
issue = {5},
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journal = {Phys. Rev. Lett.},
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||
month = {Mar},
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||
numpages = {0},
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||
pages = {159--162},
|
||
publisher = {American Physical Society},
|
||
title = {Effect of Correlation on the Ferromagnetism of Transition Metals},
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||
url = {https://link.aps.org/doi/10.1103/PhysRevLett.10.159},
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||
volume = {10},
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year = {1963},
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bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.10.159},
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bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.10.159}}
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||
|
||
@techreport{Kalos_2000,
|
||
author = {M. H. Kalos},
|
||
institution = {University of North Texas Libraries, UNT Digital Library},
|
||
title = {Domain Green's Function Sampling in Diffusion Monte Carlo},
|
||
year = {2000}}
|
||
|
||
@phdthesis{Assaraf_PhD,
|
||
address = {Paris},
|
||
author = {R. Assaraf},
|
||
date-modified = {2022-09-15 09:18:33 +0200},
|
||
school = {Universit\'e d Pierre et Marie Curie},
|
||
title = {M\'ethodes Monte Carlo quantique. D\'eveloppements et applications \`a quelques probl\`emes quantiques fortement corr\'el\'es.},
|
||
year = {1999}}
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|
||
@article{Kalos_1974,
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author = {Kalos, M. H. and Levesque, D. and Verlet, L.},
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doi = {10.1103/PhysRevA.9.2178},
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issue = {5},
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journal = {Phys. Rev. A},
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month = {May},
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numpages = {0},
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pages = {2178--2195},
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publisher = {American Physical Society},
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||
title = {Helium at zero temperature with hard-sphere and other forces},
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url = {https://link.aps.org/doi/10.1103/PhysRevA.9.2178},
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volume = {9},
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year = {1974},
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bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.9.2178},
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bdsk-url-2 = {https://doi.org/10.1103/PhysRevA.9.2178}}
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|
||
@article{Assaraf_1999A,
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author = {Assaraf, Roland and Caffarel, Michel},
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date-modified = {2022-09-15 09:18:50 +0200},
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doi = {10.1103/PhysRevLett.83.4682},
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issue = {23},
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journal = {Phys. Rev. Lett.},
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month = {Dec},
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numpages = {0},
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||
pages = {4682--4685},
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||
publisher = {American Physical Society},
|
||
title = {Zero-Variance Principle for Monte Carlo Algorithms},
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||
url = {https://link.aps.org/doi/10.1103/PhysRevLett.83.4682},
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volume = {83},
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year = {1999},
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bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.83.4682},
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bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.83.4682}}
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@article{Caffarel_1988,
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author = {Caffarel,Michel and Claverie,Pierre},
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date-modified = {2022-09-15 10:16:31 +0200},
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doi = {10.1063/1.454227},
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journal = {J. Chem. Phys.},
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number = {2},
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pages = {1088-1099},
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title = {Development of a pure diffusion quantum Monte Carlo method using a full generalized Feynman--Kac formula. I. Formalism},
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volume = {88},
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year = {1988},
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bdsk-url-1 = {https://doi.org/10.1063/1.454227}}
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@article{Baroni_1999,
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author = {Baroni, Stefano and Moroni, Saverio},
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doi = {10.1103/PhysRevLett.82.4745},
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journal = {Phys. Rev. Lett.},
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numpages = {0},
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pages = {4745--4748},
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publisher = {American Physical Society},
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title = {Reptation Quantum Monte Carlo: A Method for Unbiased Ground-State Averages and Imaginary-Time Correlations},
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url = {https://link.aps.org/doi/10.1103/PhysRevLett.82.4745},
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volume = {82},
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year = {1999},
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bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.82.4745},
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bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.82.4745}}
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@article{Sorella_1998,
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author = {Sorella, Sandro},
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issue = {20},
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journal = {Phys. Rev. Lett.},
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month = {May},
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numpages = {0},
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pages = {4558--4561},
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publisher = {American Physical Society},
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title = {Green Function Monte Carlo with Stochastic Reconfiguration},
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url = {https://link.aps.org/doi/10.1103/PhysRevLett.80.4558},
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volume = {80},
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year = {1998},
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bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.80.4558},
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bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.80.4558}}
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@book{Golub_2012,
|
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author = {Golub, Gene H. and Van Loan, Charles F.},
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edition = {Fourth},
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publisher = {The Johns Hopkins University Press},
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title = {Matrix Computations},
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year = {2012}}
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||
|
||
@book{Ceperley_1979,
|
||
author = {D.M. Ceperley and M.H Kalos},
|
||
chapter = {4},
|
||
editor = {K.Binder},
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||
publisher = {Springer, Berlin},
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||
title = {Monte Carlo Methods in Statistical Physics},
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year = {1979}}
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@article{Carlson_2007,
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author = {J. Carlson},
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date-modified = {2022-09-15 10:14:32 +0200},
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doi = {10.1016/j.nuclphysa.2006.12.079},
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journal = {Nucl. Physics. A},
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pages = {516},
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title = {Recent Progress in Quantum Monte Carlo Calculations of Nuclear Structure and Reactions},
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volume = {787},
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year = {2007},
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bdsk-url-1 = {https://doi.org/10.1016/j.nuclphysa.2006.12.079}}
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@article{Davidson_1975,
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author = {E. R. Davidson},
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date-modified = {2022-09-15 10:15:55 +0200},
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doi = {10.1016/0021-9991(75)90065-0},
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journal = {J. Comput. Phys.},
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||
pages = {87-94},
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||
title = {The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices},
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volume = {17},
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||
year = {1975},
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bdsk-url-1 = {https://doi.org/10.1016/0021-9991(75)90065-0}}
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@article{Holzmann_2006,
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author = {Holzmann, Markus and Bernu, Bernard and Ceperley, D. M.},
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date-modified = {2022-09-15 10:25:57 +0200},
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||
doi = {10.1103/PhysRevB.74.104510},
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journal = {Phys. Rev. B},
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pages = {104510},
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title = {Many-body wavefunctions for normal liquid $^{3}\mathrm{He}$},
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volume = {74},
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year = {2006},
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bdsk-url-1 = {https://doi.org/10.1103/PhysRevB.74.104510}}
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@article{Foulkes_2001,
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author = {Foulkes, W. M. C. and Mitas, L. and Needs, R. J. and Rajagopal, G.},
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doi = {10.1103/RevModPhys.73.33},
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issue = {1},
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journal = {Rev. Mod. Phys.},
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month = {Jan},
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numpages = {0},
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||
pages = {33--83},
|
||
publisher = {American Physical Society},
|
||
title = {Quantum Monte Carlo simulations of solids},
|
||
url = {https://link.aps.org/doi/10.1103/RevModPhys.73.33},
|
||
volume = {73},
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||
year = {2001},
|
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bdsk-url-1 = {https://link.aps.org/doi/10.1103/RevModPhys.73.33},
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