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

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

2009-09-16

arxiv.org/abs/0909.3031v1

Physics

Condensed Matter

Statistical Mechanics

4+ pages, 5 figures

Scientific paper

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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