Predicting topological quantum phase transition from dynamics via multisite entanglement

TL;DR

This paper demonstrates that dynamical measures like Loschmidt echo and multipartite entanglement can effectively identify topological quantum phase transitions in a Kitaev model, even under dissipation.

Contribution

It introduces a method to detect topological phase transitions through dynamical entanglement measures in a solvable Kitaev model, including effects of thermal baths.

Findings

Dynamical quantifiers distinguish topological phases from non-topological ones.

Derivatives of dynamical measures faithfully identify the phase transition.

Block entanglement in dissipative dynamics can differentiate initial equilibrium phases.

Abstract

An exactly solvable Kitaev model in a two-dimensional square lattice exhibits a topological quantum phase transition which is different from the symmetry-breaking transition at zero temperature. When the ground state of a nonlinearly perturbed Kitaev model with different strengths of perturbation taken as the initial state is quenched to a pure Kitaev model, we demonstrate that various features of the dynamical state, such as the Loschmidt echo and time-averaged multipartite entanglement, can determine whether the initial state belongs to the topological phase or not. Moreover, the derivatives of the dynamical quantifiers can faithfully identify the topological quantum phase transition, which is present at equilibrium. When the individual qubits of the lattice interact with the local thermal bath repeatedly, we observe that block entanglement in dissipative dynamics can nevertheless distinguish the equilibrium phases from which the system starts evolution.