Fidelity susceptibility made simple: A unified quantum Monte Carlo approach

TL;DR

This paper introduces a universal quantum Monte Carlo method to efficiently compute fidelity susceptibility, a key indicator of phase transitions, applicable to various quantum many-body systems at different temperatures.

Contribution

It presents a generic, efficient approach to evaluate fidelity susceptibility across diverse quantum systems within Monte Carlo simulations, including ground and finite temperature cases.

Findings

Successfully applied to Bose-Hubbard and XXZ models

Revealed insights into the spin-liquid phase in the Hubbard model

Provided a simple, universal Monte Carlo estimator for fidelity susceptibility

Abstract

The fidelity susceptibility is a general purpose probe of phase transitions. With its origin in quantum information and in the differential geometry perspective of quantum states, the fidelity susceptibility can indicate the presence of a phase transition without prior knowledge of the local order parameter, as well as reveal the universal properties of a critical point. The wide applicability of the fidelity susceptibility to quantum many-body systems is, however, hindered by the limited computational tools to evaluate it. We present a generic, efficient, and elegant approach to compute the fidelity susceptibility of correlated fermions, bosons, and quantum spin systems in a broad range of quantum Monte Carlo methods. It can be applied both to the ground-state and non-zero temperature cases. The Monte Carlo estimator has a simple yet universal form, which can be efficiently evaluated in simulations. We demonstrate the power of this approach with applications to the Bose-Hubbard model, the spin-$1/2$ XXZ model, and use it to examine the hypothetical intermediate spin-liquid phase in the Hubbard model on the honeycomb lattice.