Spontaneous symmetry breaking and bifurcations in ground state fidelity for quantum lattice systems

TL;DR

This paper demonstrates that the ground state fidelity per lattice site universally signals spontaneous symmetry breaking and bifurcations during quantum phase transitions in lattice systems, using tensor network algorithms.

Contribution

It introduces the use of ground state fidelity per lattice site as a universal indicator of symmetry breaking in quantum lattice systems, applicable via tensor network methods.

Findings

Fidelity per lattice site exhibits bifurcations at quantum critical points.

The approach is model-independent and applicable to various quantum lattice models.

Tensor network algorithms enable computation on infinite-size lattices.

Abstract

Spontaneous symmetry breaking occurs in a system when its Hamiltonian possesses a certain symmetry, whereas the ground state wave functions do not preserve it. This provides such a scenario that a bifurcation, which breaks the symmetry, occurs when some control parameter crosses its critical value. It is unveiled that the ground state fidelity per lattice site exhibits such a bifurcation for quantum lattice systems undergoing quantum phase transitions. The significance of this result lies in the fact that the ground state fidelity per lattice site is \textit{universal}, in the sense that it is model-independent, in contrast to (model-dependent) order parameters. This fundamental quantity may be computed by exploiting the newly-developed tensor network algorithms on infinite-size lattices. We illustrate the scheme in terms of the quantum Ising model in a transverse magnetic field and the spin 1/2 XYX model in an external magnetic field on an infinite-size lattice in one spatial dimension.