Tackling the Sign Problem in the Doped Hubbard Model with Normalizing Flows

2026-03-18

AI Summary

This work addresses the severe sign problem and poor ergodicity that hinder quantum Monte Carlo simulations of the doped Hubbard model at finite chemical potential. To overcome these challenges, the authors propose a normalized flow approach combined with an annealing strategy, enabling efficient and ergodic sampling in the spin basis. This method extends normalized flows—previously limited to half-filling—to the finite chemical potential regime, circumventing the ergodicity constraints and exacerbated sign problem inherent in conventional charge-basis hybrid Monte Carlo schemes. Numerical experiments demonstrate that the proposed approach reduces statistical errors by an order of magnitude compared to existing methods and accurately reproduces exact diagonalization results, thereby significantly enhancing both the efficiency and precision of simulations for doped correlated electron systems.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

The Hubbard model at finite chemical potential is a cornerstone for understanding doped correlated systems, but simulations are severely limited by the sign problem. In the auxiliary-field formulation, the spin basis mitigates the sign problem, yet severe ergodicity issues have limited its use. We extend recent advances with normalizing flows at half-filling to finite chemical potential by introducing an annealing scheme enabling ergodic sampling. Compared to state-of-the-art hybrid Monte Carlo in the charge basis, our approach accurately reproduces exact diagonalization results while reducing statistical uncertainties by an order of magnitude, opening a new path for simulations of doped correlated systems.

Problem

• sign problem
• doped Hubbard model
• ergodicity
• finite chemical potential
• auxiliary-field formulation

Innovation

• normalizing flows
• sign problem
• Hubbard model
• annealing scheme
• ergodicity