High-order fidelity and quantum phase transition for the Heisenberg chain with next-nearest-neighbor interaction

TL;DR

This paper investigates how high-order fidelity measures can detect quantum phase transitions in a Heisenberg chain with next-nearest-neighbor interactions, especially of the BKT type, highlighting the limitations of fidelity susceptibility.

Contribution

It introduces the use of higher-order ground-state fidelity to effectively identify BKT-type quantum phase transitions in finite-size Heisenberg chains.

Findings

Fidelity susceptibility alone does not clearly indicate the phase transition point.

Higher-order fidelity terms can effectively detect the quantum phase transition.

The study provides a new approach for analyzing phase transitions in quantum many-body systems.

Abstract

In this article, we study the high order term of the fidelity of the Heisenberg chain with next-nearest-neighbor interaction and analyze its connection with quantum phase transition of Beresinskii-Kosterlitz-Thouless type happened in the system. We calculate the fidelity susceptibility of the system and find that although the phase transition point can't be well characterized by the fidelity susceptibility, it can be effectively picked out by the higher order of the ground-state fidelity for finite-size systems.