Many-body quantum sign structures as non-glassy Ising models

TL;DR

This paper demonstrates that the sign structure of ground states in frustrated quantum spin systems can be efficiently reconstructed by mapping to a classical Ising model, revealing an underlying simplicity despite quantum frustration.

Contribution

The authors introduce a method to bootstrap quantum sign structures from amplitudes by mapping to a classical Ising model, which is solvable efficiently even for frustrated systems.

Findings

Sign structures can be reconstructed from amplitudes using an Ising model mapping.

The Ising model remains largely unfrustrated even for highly frustrated quantum systems.

A deterministic $O(K\,\log K)$ algorithm efficiently solves the classical Ising problem.

Abstract

The non-trivial phase structure of the eigenstates of many-body quantum systems severely limits the applicability of quantum Monte Carlo, variational, and machine learning methods. Here, we study real-valued signful ground-state wave functions of frustrated quantum spin systems and, assuming that the tasks of finding wave function amplitudes and signs can be separated, show that the signs can be easily bootstrapped from the amplitudes. We map the problem of finding the sign structure to an auxiliary classical Ising model defined on a subset of the Hilbert space basis. We show that the Ising model does not exhibit significant frustrations even for highly frustrated parental quantum systems, and is solvable with a fully deterministic $O(K\log K)$-time combinatorial algorithm (where $K$ is the Ising model size). Given the ground state amplitudes, we reconstruct the signs of the ground states of several frustrated quantum models, thereby revealing the hidden simplicity of many-body sign structures.