2-D Quantum Ising Model Fidelity and Order Parameter

Abstract

Abstract This paper explores an interesting relationship between the ground-state fidelity quantum phase transitions and bifurcations per lattice site, and proposes a universal order parameter for the quantum Ising model for a square lattice of infinite-size in two spatial dimensions as a prototype model with symmetry breaking order. The approach is based on computing ground-state wave functions using a tensor network algorithm utilizing a representation with infinite projected entangled-pair states. The results can be applied to any systems with symmetry breaking order, because in the conventional Landau-Ginzburg-Wilson paradigm a quantum system subjected to a phase transition exhibits spontaneous symmetry breaking quantified by a local order parameter. A reduced fidelity bifurcation between two different reduced density matrices is also explored.