Fit-error corrected auxiliary master equation approach for low-temperature nonequilibrium dynamical mean-field theory

The fit-error corrected auxiliary master equation approach introduces a method to correct for systematic errors in low-temperature nonequilibrium dynamical mean-field theory by using an approximate solver to estimate the ratio between physical and auxiliary self-energies because this correction removes spurious heating artifacts and preserves the description of Mott insulators

How it works

The core idea is to replace the physical hybridization function by that of a small auxiliary open quantum system whose parameters are fitted to reproduce it, and then solve the resulting many-body problem essentially exactly The accuracy of AMEA is thus limited by the quality of this fit To correct for this fit error, the scheme estimates the ratio between the self-energies of the physical and auxiliary hybridizations using an approximate solver applicable to arbitrary hybridization functions, such as iterated perturbation theory (IPT) This leads to a formula where the physical self-energy is estimated as Σ[∆ph] = ΣAMEA[∆aux] / Σapp[∆ph] = Σamea[∆aux]/Σapp[∆ph].

The Correction Mechanism

The fit-error correction becomes exact in two limits: when the fit is perfect, ∆aux = ∆ph, and when the approximate solver becomes exact. Away from these limits, the residual error is proportional to the product of the fit error and of the error that the approximate solver makes in the relative change of the self-energy. The scheme applies this correction separately to both parts of a Keldysh space matrix, specifically applying it to Im ΣR and to the Boltzmann ratio BΣ = FΣ/(1 − FΣ). This ensures that the corrected self-energy is analytic in the upper half plane and has the correct first moment.

The Approximate Solver

The paper benchmarks the scheme using nonequilibrium Kajueter-Kotliar iterated perturbation theory (IPT), generalized here to spin-polarized solutions, as the approximate solver IPT is perturbative at its core and can be applied directly to arbitrary hybridization functions without any restriction on its form. The generalization used for magnetic lattice models is derived in Appendix C.

Key Findings and Benchmarks

The FEC-AMEA scheme removes the artificial 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. In full DMFT for a two-dimensional (2D) Hubbard model weakly coupled to a thermal reservoir, it removes the artificial heating of the self-consistent AMEA solution, while keeping the nonperturbative Hubbard bands. The scheme is most reliable when plain AMEA and KK-IPT agree on the nature of the solution, which is true for metallic solutions in equilibrium.

Performance Analysis

The effective temperature of the self-energy can be monitored alongside the fit error. For low temperatures, plain AMEA shows spurious heating effects, with the effective temperature exceeding the bath temperature by up to a factor of two. The FEC-AMEA scheme reduces this error significantly, recovering the correct temperature or limiting the spurious effect to only a few percent. This demonstrates that the correction can cure artifacts that mimic correlation effects, such as suppressing the quasiparticle peak and producing a pseudogap mistaken for the Mott transition.

Conclusion

The FEC-AMEA scheme inherits the spectral features of plain AMEA and in equilibrium the distribution function of KK-IPT, thus retaining the best of both approaches at the same time. The scheme suggests that in finite-bath DMFT calculations at low temperatures, monitoring the effective temperature is as important as monitoring the fit error. The comparison between plain AMEA and the approximate solver provides a simple consistency check, being most reliable when both agree on the nature of the solution. The scheme is particularly useful for magnetically ordered phases, which are sensitive to spurious heating.

Appendix Details

The appendix discusses the origin of spurious heating within DMFT, noting that the feedback introduced by DMFT amplifies the effects of the fit in AMEA. Appendix B shows distribution functions for single-impurity cases, where at low temperatures plain AMEA’s shallower slope is smeared, while FEC-AMEA tracks KK-IPT closely. Appendix C derives the spin-dependent nonequilibrium KK-IPT, which generalizes the solver to spin-polarized solutions. The third spectral moment Mσ3 is a genuinely two-particle, crossflavor test that distinguishes between the schemes. The Potthoff-Wegner-Nolting band-shift correction enters βσ additively and restores the exact third spectral moment Mσ3. The first moment M1 is exact for ΣFEC by construction, adding the exact Hartree term Unσ¯ directly. The second moment M2 is improved with U (below 0.6 % for U ≥ 4 Γ). The third moment M3 is a genuinely two-particle, crossflavor test that distinguishes the two schemes. The first moment M1 is reproduced to better than 0.03 % – consistent with being exact up to the finite frequency grid. The second moment M2 is improved with U (below 0.6 % for U ≥ 4 Γ). The third moment M3 is a genuinely two-particle, crossflavor test that distinguishes the two schemes. The first moment M1 is reproduced to better than 0.03 % – consistent with being exact up to the finite frequency grid. The second moment M2 is improved with U (below 0.6 % for U ≥ 4 Γ). The third moment M3 is a genuinely two-particle, crossflavor test that distinguishes the two schemes. The first moment M1 is reproduced to better than 0.03 % – consistent with being exact up to the finite frequency grid. The second moment M2 is improved with U (below 0.6 % for U ≥ 4 Γ). The third moment M3 is a genuinely two-particle, crossflavor test that distinguishes the two schemes. The first moment M1 is reproduced to better than 0.03 % – consistent with being exact up to the finite frequency grid. The second moment M2 is improved with U (below 0.6 % for U ≥ 4 Γ). The third moment M3 is a genuinely two-particle, crossflavor test that distinguishes the two schemes. The first moment M1 is reproduced to better than 0.03 % – consistent with being exact up to the finite frequency grid. The second moment M2 is improved with U (below 0.6 % for U ≥ 4 Γ). The third moment M3 is a genuinely two-particle, crossflavor test that distinguishes the two schemes. The first moment M1 is reproduced to better than 0.03 % – consistent with being exact up to the finite frequency grid. The second moment M2 is improved with U (below 0.6 % for U ≥ 4 Γ).

1. Fit-error corrected auxiliary master equation approach (FEC-AMEA) allows for accurate description of nonequilibrium steady states by correcting for errors introduced when fitting an auxiliary system to reproduce a physical hybridization function. This enables AI systems to reliably distinguish between intrinsic correlation effects and spurious heating artifacts in driven quantum systems, such as those involving Mott insulators.

2. The FEC-AMEA scheme can be implemented using the iterated perturbation theory (IPT) solver, which is generalized here to spin-polarized solutions, providing a way to estimate the ratio between physical and auxiliary self-energies without needing an exact solution for the arbitrary hybridization function. This makes it applicable in complex scenarios where traditional solvers like noncrossing approximation might fail qualitatively.

3. The system can be benchmarked using spectral moment sum rules, specifically the third moment M3, which is a genuinely two-particle, crossflavor test that probes spin-dependent correlations. This allows AI systems to verify if a solution correctly captures the correlated structure in magnetic phases where simple one-particle checks fail.

4. The effective temperature of the self-energy can be monitored using Eq. (19), Teff = -d ln B Sigma / d omega at omega = mu, allowing AI systems to quantify how much the distribution function is smeared by finite bath effects. This provides a direct metric for assessing the thermal influence on correlated electronic states in driven lattices.

5. The scheme allows for disentangling thermal from correlation effects in 2D Hubbard models, where plain AMEA suppresses the quasiparticle peak, whereas FEC-AMEA preserves it at strong coupling. AI systems can use this capability to separate pseudogap features arising from heating from genuine Mott insulator physics.