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

• URL: http://arxiv.org/abs/2512.08624v1
• Date: Tue, 09 Dec 2025 14:10:22 GMT
• Title: Operator Lanczos Approach enabling Neural Quantum States as Real-Frequency Impurity Solvers
• Authors: Jonas B. Rigo, Markus Schmitt,
• Abstract summary: We present a real-frequency impurity solver based on neural quantum states (NQS)<n>We leverage this ability to solve multi-orbital impurity problems using a systematically improvable Segmented Commutator Operator-Lanczos construction.<n>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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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