Universal construction of order parameters for translation-invariant quantum lattice systems with symmetry-breaking order

TL;DR

This paper introduces a universal method to construct order parameters for quantum phase transitions in translation-invariant systems with symmetry-breaking, using fidelity measures and tensor networks, applicable to various models.

Contribution

It proposes a practical, universal construction of order parameters based on fidelity and tensor networks for symmetry-breaking quantum phase transitions.

Findings

Successfully applied to quantum Ising, XYX, and XXZ models.

Identifies symmetry-breaking phases using fidelity-based order parameters.

Provides insights into factorized states in quantum systems.

Abstract

For any translation-invariant quantum lattice system with a symmetry group G, we propose a practical and universal construction of order parameters which identify quantum phase transitions with symmetry-breaking order. They are defined in terms of the fidelity between a ground state and its symmetry-transformed counterpart, and are computed through tensor network representations of the ground-state wavefunction. To illustrate our scheme, we consider three quantum systems on an infinite lattice in one spatial dimension, namely, the quantum Ising model in a transverse magnetic field, the quantum spin-1/2 XYX model in an external magnetic field, and the quantum spin-1 XXZ model with single-ion anisotropy. All these models have symmetry group Z_2 and exhibit broken-symmetry phases. We also discuss the role of the order parameters in identifying factorized states.