Bifurcation in ground-state fidelity and universal order parameter for two-dimensional quantum transverse Ising model

TL;DR

This paper links quantum phase transitions to bifurcations in ground-state fidelity and introduces a universal order parameter for the 2D quantum Ising model, using tensor network algorithms on an infinite lattice.

Contribution

It constructs a universal order parameter for the 2D quantum Ising model and connects fidelity bifurcations to phase transitions using tensor network methods.

Findings

Ground-state fidelity bifurcates at phase transition points

Universal order parameter is constructed for the 2D quantum Ising model

Fidelity analysis applies to systems with symmetry breaking order

Abstract

We establish an intriguing connection between quantum phase transitions and bifurcations in the ground-state fidelity per lattice site, and construct the universal order parameter for quantum Ising model in a transverse magnetic field on an infinite-size square lattice in two spatial dimensions, a prototypical model with symmetry breaking order. This is achieved by computing ground-state wave functions in the context of the tensor network algorithm based on the infinite projected entangled-pair state representation. Our finding is applicable to any systems with symmetry breaking order, as a result of the fact that, in the conventional Landau-Ginzburg-Wilson paradigm, a quantum system undergoing a phase transition is characterized in terms of spontaneous symmetry breaking captured by a local order parameter. In addition, a bifurcation in the reduced fidelity between two different reduced density matrices is also discussed.