A universal black-box quantum Monte Carlo approach to quantum phase transitions

TL;DR

This paper introduces a universal, black-box quantum Monte Carlo method for studying quantum phase transitions, capable of handling various models without prior knowledge of order parameters or custom updates.

Contribution

It presents exact, closed-form estimators for energy and fidelity susceptibilities applicable to a wide range of Hamiltonians, simplifying quantum phase transition analysis.

Findings

Successfully applied to transverse-field Ising model

Extended to XXZ model and models with random unitaries

Demonstrates broad applicability and efficiency of the method

Abstract

We derive exact, universal, closed-form quantum Monte Carlo estimators for finite-temperature energy susceptibility and fidelity susceptibility, applicable to essentially arbitrary Hamiltonians. Combined with recent advancements in Monte Carlo, our approach enables a black-box framework for studying quantum phase transitions--without requiring prior knowledge of an order parameter or the manual design of model-specific ergodic quantum Monte Carlo update rules. We demonstrate the utility of our method by applying a single implementation to the transverse-field Ising model, the XXZ model, and an ensemble of models related by random unitaries.