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48 lines
1.7 KiB
ReStructuredText
48 lines
1.7 KiB
ReStructuredText
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Tour 3: Solving a quantum impurity model with QMC
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----------------------------------------------------------
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Free electrons are nice, but the `I` in TRIQS means `interacting`.
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So let us solve a simple one-band Anderson impurity model
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.. math::
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\mathcal{H}_\mathrm{loc} = U n_\uparrow n_\downarrow,
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where the non-interacting Green's function is:
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.. math::
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G^{-1}_{0,\sigma} (i \omega_n) = i \omega_n - \epsilon_f - V^2 \Gamma_\sigma(i \omega_n).
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In this example, an impurity with the non-interacting level position at energy :math:`\epsilon_f` and on-site Coulomb repulsion :math:`U` is embedded into an electronic bath.
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The
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electronic bath has a flat density of states over the interval
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:math:`[-1,1]` and hybridizes with the impurity with the amplitude :math:`V`.
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We solve this model using the hybridization expansion Continuous Time Quantum Monte Carlo method (CT-Hyb)
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proposed by `P. Werner et al. <http://link.aps.org/doi/10.1103/PhysRevLett.97.076405>`_
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To this end we first initialize the ``Solver`` class of the TRIQS CT-Hyb implementaion
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``pytriqs.applications.impurity_solvers.ctqmc_hyb``.
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Then, after having constructed the non-interacting Green's function :math:`G^{-1}_{0,\sigma}`,
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we launch the CT-Hyb calculations by calling the ``Solve`` method of the ``Solver`` class.
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Finally, the resulting interacting Green's function as well as average impurity occupancy
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is stored in the :ref:`HDF5 format<hdf5_base>`.
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.. literalinclude:: ../solvers/aim.py
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The result can be then read from the ``HDF5`` file and plotted using the ``oplot`` function:
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.. literalinclude:: aim_plot.py
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.. image:: aim_plot1.png
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:width: 700
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:align: center
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We go through this example in more details in the tutorial :ref:`Anderson impurity model <aim>`
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