Operator Lanczos Approach enabling Neural Quantum States as Real-Frequency Impurity Solvers

TL;DR

This paper introduces a neural quantum state-based impurity solver using operator-Lanczos methods, enabling accurate real-frequency spectral calculations for multi-orbital models in dynamical mean-field theory.

Contribution

It develops a novel neural quantum state approach combined with a systematic operator-Lanczos construction for solving multi-orbital impurity problems in DMFT.

Findings

Achieves high-precision ground states for Anderson and Hubbard-Kanamori models.

Accurately resolves zero-temperature spectral functions and self-energies.

Demonstrates potential for extending DMFT to complex correlated systems.

Abstract

To understand the intricate exchange between electrons of different bands in strongly correlated materials, it is essential to treat multi-orbital models accurately. For this purpose, dynamical mean-field theory (DMFT) provides an established framework, whose scope crucially hinges on the availability of efficient quantum impurity solvers. Here we present a real-frequency impurity solver based on neural quantum states (NQS) combined with an operator-Lanczos construction. NQS are an asymptotically unbiased variational ground-state ansatz that employs neural networks to capture long-range correlations on complicated graph structures. We leverage this ability to solve multi-orbital impurity problems using a systematically improvable Segmented Commutator Operator-Lanczos (SCOL) construction. Our benchmarks on both the single-orbital Anderson model and the multi-orbital Hubbard-Kanamori impurity Hamiltonian reveal excellent ground-state precision and the capacity to accurately resolve zero temperature spectral functions and self-energies. These results open avenues for extending DMFT to more challenging problems.