Ground-state fidelity in one-dimensional gapless model

TL;DR

This paper establishes a relation between quantum phase transitions and fidelity susceptibility, deriving formulas for 1D gapless systems, and demonstrates that fidelity susceptibility can signal various quantum phase transitions, including BKT types.

Contribution

It provides a general relation between quantum phase transitions and fidelity susceptibility, and derives formulas for Tomonaga-Luttinger liquids, showing their effectiveness in detecting phase transitions.

Findings

Fidelity susceptibility signals quantum phase transitions.

Derived formulas for fidelity in Tomonaga-Luttinger liquids.

Validated the approach on the 1D XXZ model.

Abstract

A general relation between quantum phase transitions and the second derivative of the fidelity (or the "fidelity susceptibility") is proposed. The validity and the limitation of the fidelity susceptibility in characterizing quantum phase transitions is thus established. Moreover, based on the bosonization method, general formulas of the fidelity and the fidelity susceptibility are obtained for a class of one-dimensional gapless systems known as the Tomonaga-Luttinger liquid. Applying these formulas to the one-dimensional spin-1/2 $XXZ$ model, we find that quantum phase transitions, even of the Beresinskii-Kosterlitz-Thouless type, can be signaled by the fidelity susceptibility.