Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions

TL;DR

This paper introduces two Quantum Monte Carlo methods to compute fidelity and its susceptibility in large many-body systems, demonstrating their effectiveness on a 2D Heisenberg model with quantum phase transitions and establishing a scaling theory relating fidelity divergence to critical exponents.

Contribution

The paper presents novel Quantum Monte Carlo schemes for fidelity calculation in large systems and develops a scaling theory linking fidelity susceptibility to critical exponents.

Findings

Fidelity estimators detect quantum phase transitions in the 2D Heisenberg model.

The scaling theory accurately relates fidelity susceptibility divergence to critical exponents.

Numerical results agree well with the theoretical predictions.

Abstract

When a system undergoes a quantum phase transition, the ground-state wave-function shows a change of nature, which can be monitored using the fidelity concept. We introduce two Quantum Monte Carlo schemes that allow the computation of fidelity and its susceptibility for large interacting many-body systems. These methods are illustrated on a two-dimensional Heisenberg model, where fidelity estimators show marked behaviours at two successive quantum phase transitions. We also develop a scaling theory which relates the divergence of the fidelity susceptibility to the critical exponent of the correlation length. A good agreement is found with the numerical results.