Quantum Critical Scaling of Fidelity Susceptibility

TL;DR

This paper derives new scaling relations for fidelity susceptibility near quantum critical points, expressed solely in terms of critical exponents, and validates them through quantum Monte Carlo simulations of the transverse-field Ising model.

Contribution

It introduces a quantum Monte Carlo scheme to evaluate fidelity susceptibility and establishes scaling relations based only on conventional critical exponents.

Findings

Scaling relations accurately describe fidelity susceptibility near criticality.

Numerical results confirm the validity of the derived scaling relations.

Ground-state energy's second derivative serves as an alternative indicator of quantum criticality.

Abstract

The behavior of the ground-state fidelity susceptibility in the vicinity of a quantum critical point is investigated. We derive scaling relations describing its singular behavior in the quantum critical regime. Unlike it has been found in previous studies, these relations are solely expressed in terms of conventional critical exponents. We also describe in detail a quantum Monte Carlo scheme that allows for the evaluation of the fidelity susceptibility for a large class of many-body systems and apply it in the study of the quantum phase transition for the transverse-field Ising model on the square lattice. Finite size analysis applied to the so obtained numerical results confirm the validity of our scaling relations. Furthermore, we analyze the properties of a closely related quantity, the ground-state energy's second derivative, that can be numerically evaluated in a particularly efficient way. The usefulness of both quantities as alternative indicators of quantum criticality is examined.