Fit-error corrected auxiliary master equation approach for low-temperature nonequilibrium dynamical mean-field theory
Abstract
The auxiliary master equation approach (AMEA) is a nonperturbative impurity solver for steady-state nonequilibrium dynamical mean-field theory (DMFT). It replaces the physical hybridization function by that of a small auxiliary open quantum system, whose parameters are fitted to reproduce it, and then solves the resulting many-body problem essentially exactly. AMEA's accuracy is thus limited by the quality of this fit: since the fastest-varying part of the hybridization is set by the distribution function, whose Fermi edges sharpen at low temperature, the fit tends to overestimate the temperature, especially for weak reservoir coupling. For the auxiliary hybridization itself, however, AMEA's self-energy is essentially exact. We correct for the fit error by estimating, via an approximate solver applicable to arbitrary hybridization functions, the ratio between the self-energies of the physical and auxiliary hybridizations, and using it to extend AMEA's self-energy from the auxiliary to the physical case. This fit-error correction becomes exact whenever either the fit or the approximate solver is exact. We benchmark the scheme using the nonequilibrium Kajueter-Kotliar iterated perturbation theory (IPT), generalized here to spin-polarized solutions, as the approximate solver; other approximate solvers, such as the noncrossing approximation, can be used as well. Applied to an Anderson impurity model with a spin-polarized bath, and within DMFT to a Hubbard layer weakly coupled to two metallic reservoirs, the correction largely removes the spurious heating from the AMEA fit and from insufficient thermalization by the reservoirs, while preserving the correct description of the Mott insulator, which IPT alone cannot fully recover.
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BibTeX
@misc{fuchs2026fiterror,
title = {{Fit-error corrected auxiliary master equation approach for low-temperature nonequilibrium dynamical mean-field theory}},
author = {Sebastian Alois Fuchs and Enrico Arrigoni and Tommaso Maria Mazzocchi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30846},
eprint = {2610.30846},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30846},
}
RIS
TY - UNPB
TI - Fit-error corrected auxiliary master equation approach for low-temperature nonequilibrium dynamical mean-field theory
AU - Sebastian Alois Fuchs
AU - Enrico Arrigoni
AU - Tommaso Maria Mazzocchi
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30846
UR - https://arxiv.org/abs/2610.30846
AB - The auxiliary master equation approach (AMEA) is a nonperturbative impurity solver for steady-state nonequilibrium dynamical mean-field theory (DMFT). It replaces the physical hybridization function by that of a small auxiliary open quantum system, whose parameters are fitted to reproduce it, and then solves the resulting many-body problem essentially exactly. AMEA's accuracy is thus limited by the quality of this fit: since the fastest-varying part of the hybridization is set by the distribution function, whose Fermi edges sharpen at low temperature, the fit tends to overestimate the temperature, especially for weak reservoir coupling. For the auxiliary hybridization itself, however, AMEA's self-energy is essentially exact. We correct for the fit error by estimating, via an approximate solver applicable to arbitrary hybridization functions, the ratio between the self-energies of the physical and auxiliary hybridizations, and using it to extend AMEA's self-energy from the auxiliary to the physical case. This fit-error correction becomes exact whenever either the fit or the approximate solver is exact. We benchmark the scheme using the nonequilibrium Kajueter-Kotliar iterated perturbation theory (IPT), generalized here to spin-polarized solutions, as the approximate solver; other approximate solvers, such as the noncrossing approximation, can be used as well. Applied to an Anderson impurity model with a spin-polarized bath, and within DMFT to a Hubbard layer weakly coupled to two metallic reservoirs, the correction largely removes the spurious heating from the AMEA fit and from insufficient thermalization by the reservoirs, while preserving the correct description of the Mott insulator, which IPT alone cannot fully recover.
ER -