mirror of https://github.com/abinit/abinit.git
110 lines
6.1 KiB
Markdown
110 lines
6.1 KiB
Markdown
---
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description: How to perform a DMFT calculation
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authors: BAmadon
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---
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<!--- This is the source file for this topics. Can be edited. -->
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This page gives hints on how to perform a DMFT calculation with the ABINIT package.
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## Introduction
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DFT fails to describe the ground state and/or the excited states such as many
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lanthanides, actinides or transition metals. Indeed, exchange correlation
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functionals are not (yet) able to describe the strong repulsive Coulomb
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interactions occurring among electrons in partly filled localized d or f
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orbitals.
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A way to improve the description of strongly correlated systems is to
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explicitly include the strong repulsive Coulomb interactions in the
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Hamiltonian. Solving it in the static mean field approximation, gives the
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DFT+U method ([[cite:Anisimov1991]], [[cite:Liechtenstein1995]]), implemented
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in ABINIT [[cite:Amadon2008a]]. The Dynamical Mean Field Theory
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[[cite:Georges1996]] (DMFT), goes beyond, by solving exactly the local
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correlations for an atom in an effective field (i.e., an Anderson model). The
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effective field reproduces the effect of the surrounding correlated atoms and
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is thus self-consistently related to the solution of the Anderson model
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[[cite:Georges1996]].
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The combination of DFT with DMFT [[cite:Georges2004]], [[cite:Kotliar2006]]
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([[usedmft]]= 1) relies on:
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* The definition of correlated orbitals. In ABINIT, we use Wannier functions built using projected local orbitals
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[[cite:Amadon2008]]. Wannier functions are unitarily related to a selected set of Kohn Sham (KS) wavefunctions,
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specified in ABINIT by band indices [[dmftbandi]] and [[dmftbandf]]. As empty bands are necessary
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to build Wannier functions, it is required in DMFT calculations that the KS Hamiltonian is correctly diagonalized:
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use high values for [[nnsclo]] and [[nline]]. In order to make a first rough estimation of the orbital character
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of KS bands and choose the band index, the band structure with highlighted atomic orbital character
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(so called *fatbands* ) can be plotted, using the [[pawfatbnd]] variable.
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Band structures obtained from projected orbitals Wannier functions can also be plotted using
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[[plowan_compute]] and related variables.
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* The choice of the screened Coulomb interaction U ([[upawu]]) and J ([[jpawu]]). Note that up to version 7.10.5 (but not in later versions) [[jpawu]]= 0 is required if the density matrix in the correlated subspace is not diagonal.
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* The choice of the double counting correction [[cite:Amadon2012]]. The current default choice in ABINIT is [[dmft_dc]]= 1 which corresponds to the full localized limit.
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* The method of resolution of the Anderson model. In ABINIT, it can be the Hubbard I method
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[[cite:Amadon2012]] ([[dmft_solv]]= 2), the Continuous time Quantum Monte Carlo (CTQMC) method
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[[cite:Gull2011]],[[cite:Bieder2014]] ([[dmft_solv]]= 5) or the static mean field method ([[dmft_solv]]= 1),
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equivalent to usual DFT+U [[cite:Amadon2012]]).
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The practical solution of the DFT+DMFT scheme is usually presented as a double
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loop over, first, the local Green's function, and second the electronic local
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density [[cite:Amadon2012]]. The number of iterations of the two loops are
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determined by [[dmft_iter]] and [[nstep]]. However, in the general case, the
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most efficient way to carry out fully consistent DFT+DMFT calculations is to
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keep only the loop governed by [[nstep]], while [[dmft_iter]]=1
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[[cite:Bieder2014]], [[dmft_rslf]]= 1 (to read the self-energy file at each
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step of the DFT loop) and [[prtden]]= -1 (to be able to restart the
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calculation of each step of the DFT loop from the density file). Lastly, one
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linear and one logarithmic grid are used for Matsubara frequencies
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[[cite:Kotliar2006]] determined by [[dmft_nwli]] and [[dmft_nwlo]] (Typical
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values are 10000 and 100, but convergence should be studied). More information
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can be obtained in the log file by setting [[pawprtvol]]=3.
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The main output of the calculations are the imaginary time Green's function ,
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from which spectral functions can be obtained using an external maximum
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entropy code [[cite:Bergeron2016]], self-energies, from which quasiparticle
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renormalization weight can be extracted, the density matrix of correlated
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orbitals, and the internal energies [[cite:Amadon2006]]. The electronic
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entropic contribution to the free energy can also be obtained using
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[[dmft_entropy]] and [[dmft_nlambda]].
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The efficient CTQMC code in ABINIT, which is the most time consuming part of
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DMFT, uses the hybridization expansion [[cite:Werner2006]], [[cite:Gull2011]]
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with a _density-density_ multiorbital interaction [[cite:Gull2011]]. Moreover,
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the hybridization function [[cite:Gull2011]] is assumed to be diagonal in the
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orbital (or flavor) index. This is exact for cubic symmetry without spin orbit
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coupling but, in general, one should always check that the off-diagonal terms
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are much smaller than the diagonal ones. A link to the exact rotationally
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invariant interaction CTQMC code of the TRIQS library is also available using
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[[dmft_solv]]=7.
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As the CTQMC solver uses a Fourier transform, the time grid [[dmftqmc_l]] in
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imaginary space must be chosen so that the Nyquist frequency, defined by
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π[[dmftqmc_l]] [[tsmear]], is around 2 or 3 Ha. A convergence study should
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be performed on this variable. Moreover, the number of imaginary frequencies
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([[dmft_nwlo]]) has to be set to at least twice the value of [[dmftqmc_l]].
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Typical numbers of steps for the thermalization ([[dmftqmc_therm]]) and for
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the Monte carlo runs ([[dmftqmc_n]]) are 106 and 109 respectively. The random
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number generator can be initialized with the variable [[dmftqmc_seed]].
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Several other variables are available. [[dmftctqmc_order]] gives a histogram
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of the perturbation orders during the simulation, [[dmftctqmc_gmove]]
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customizes the global move tries (mainly useful for systems with high/low spin
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configurations), and [[dmftctqmc_meas]] sets the frequency of measurement of
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quantities.
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## Related Input Variables
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{{ related_variables }}
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## Selected Input Files
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{{ selected_input_files }}
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## Tutorials
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* [[tutorial:dmft|The tutorial on DFT+DMFT]] shows how to perform a DFT+DMFT calculation on SrVO3 using projected Wannier functions. Prerequisite: DFT+U.
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