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

Jin-Hua Liu; Qian-Qian Shi; Hong-Lei Wang; Jon Links; Huan-Qiang Zhou

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arXiv · 0909.3031

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

Jin-Hua Liu·Qian-Qian Shi·Hong-Lei Wang·Jon Links·Huan-Qiang Zhou

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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.

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Jin-Hua Liu, Qian-Qian Shi, Hong-Lei Wang, Jon Links, Huan-Qiang Zhou. 2009-09-16. Universal construction of order parameters for translation-invariant quantum lattice systems with symmetry-breaking order. https://arxiv.org/abs/0909.3031

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