Fidelity approach: the misleading role of finite size level crossing of excited energies

TL;DR

This paper investigates the effectiveness of quantum fidelity in detecting phase transitions in a complex 1D spin model, revealing its limitations for analyzing the ground-state phase diagram despite its success in identifying certain phase transitions.

Contribution

The study clarifies the role of quantum fidelity in phase transition detection, highlighting its limitations in ground-state phase diagram analysis for the spin-1/2 quantum Ising model.

Findings

Quantum fidelity detects two phase transitions effectively.

Fidelity may not be suitable for ground-state phase diagram analysis.

Fidelity's role is misleading in certain complex models.

Abstract

Here, we show that, although quantum fidelity can truly identify two quantum phase transitions of a one-dimensional spin-1/2 quantum Ising model with competing nearest and next-nearest neighbour interactions in a transverse magnetic field, it may not be a suitable approach for analyzing its ground-state phase diagram.