Quantum fidelity approach to detecting quantum phases: revisiting the bond alternating Ising chain

TL;DR

This paper uses quantum fidelity and tensor network methods to identify and characterize multiple quantum phases and phase transitions in an alternating-bond Ising chain, revealing detailed phase structure and symmetry breaking.

Contribution

It introduces a fidelity-based approach combined with order parameters to detect and distinguish multiple quantum phases and first-order transitions in the bond alternating Ising model.

Findings

Detection of doubly degenerate groundstates indicating $Z_2$ symmetry breaking

Identification of four ordered phases with distinct local order parameters

Observation of first-order phase transitions between these phases

Abstract

We demonstrate the quantum fidelity approach for exploring and mapping out quantum phases. As a simple model exhibiting a number of distinct quantum phases, we consider the alternating-bond Ising chain using the infinite time evolving block decimation method in the infinite matrix product state representation. Examining the quantum fidelity with an arbitrary reference state in the whole range of the interaction parameters leads to the explicit detection of the doubly degenerate groundstates, indicating a $Z_2$ broken symmetry. The discontinuities of the fidelity indicate a first-order quantum phase transition between the four ordered phases. In order to characterize each phase, based on the spin configurations from the spin correlations, even and odd antiferromagnetic order parameters are introduced. The four defined local order parameters are shown to characterize each phase and to exhibit first-order quantum phase transitions between the ordered phases.