Quantum critical scaling of fidelity susceptibility

TLDR

The study investigates the behavior of ground‑state fidelity susceptibility near a quantum critical point and evaluates its usefulness as an alternative indicator of quantum criticality. The authors employ a quantum Monte Carlo scheme to compute fidelity susceptibility and the ground‑state energy’s second derivative for many‑body systems, applying it to the transverse‑field Ising model on a square lattice. They derive scaling relations for fidelity susceptibility expressed solely in conventional critical exponents, and finite‑size analysis confirms their validity.

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.