Stability of Global Entanglement in Thermal States of Spin Chains

Published

October 12, 2021

Author(s)

G K. Brennen, Stephen Bullock

Abstract

We investigate the entanglement properties of a one dimensional chain of spin qubits coupled via nearest neighbor interactions. The entanglement measure used is the $n$-concurrence, which is distinct from other measures on spin chains such as bipartite entanglement in that it can quantify ''global entanglement across the spin chain. Specifically, it computes the overlap of a quantum state with its time-reversed state. As such this measure is well suited to study ground states of spin chain Hamiltonians that are intrinsically time reversal symmetric. We study the robustness of $n$-concurrence of ground states when the interaction is subject to a time reversal antisymmetric magnetic field perturbation. The $n$-concurrence in the ground state of isotropic XX model is computed and it is shown that there is a critical magnetic field strength at which the entanglement experiences a jump discontinuity from the maximum value to zero. The $n$-concurrence for thermal mixed states is derived and a threshold temperature is computed below which the system has non zero entanglement.

Citation

Physical Review A (Atomic, Molecular and Optical Physics)

Pub Type

Journals

Keywords

entanglement, quantum information, statistical mechanics

Citation

Brennen, G. and Bullock, S. (2021), Stability of Global Entanglement in Thermal States of Spin Chains, Physical Review A (Atomic, Molecular and Optical Physics) (Accessed February 12, 2025)