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

2009/09/16 by Jinhua Liu, Liu, Jin-Hua, Qian‐Qian Shi +7
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum chaos and dynamical systems #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el)

paper · pdf · doi:10.48550/arxiv.0909.3031

openalex publication_date 2009/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Z₂ and exhibit broken-symmetry phases. We also discuss the role of the order parameters in identifying factorized states.

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