Magnetic quantum correlation in the 1D transverse-field XXZ model

TL;DR

This study analytically investigates quantum correlations, including entanglement and discord, in a 1D XXZ spin chain under a transverse magnetic field, revealing discord's superior ability to detect critical points over entanglement, especially at longer distances and finite temperatures.

Contribution

It provides analytical expressions for quantum correlations at any distance in the 1D XXZ model, highlighting quantum discord's effectiveness in identifying critical points beyond nearest neighbors.

Findings

Quantum discord detects critical points at longer distances where entanglement does not.

Quantum discord decays algebraically with distance in critical regimes.

Thermal quantum discord shows distinctive behavior at critical points even at finite temperature.

Abstract

One-dimensional spin-1/2 systems are well-known candidates to study the quantum correlations between particles. In the condensed matter physics, studies often are restricted to the 1st neighbor particles. In this work, we consider the 1D XXZ model in a transverse magnetic field (TF) which is not integrable except at specific points. Analytical expressions for quantum correlations (entanglement and quantum discord) between spin pairs at any distance are obtained for both zero and finite temperature, using an analytical approach proposed by Caux et al. [PRB 68, 134431 (2003)]. We compare the efficiency of the QD with respect to the entanglement in the detection of critical points (CPs) as the neighboring spin pairs go farther than the next nearest neighbors. In the absence of the TF and at zero temperature, we show that the QD for spin pairs farther than the 2nd neighbors is able to capture the critical points while the pairwise entanglement is absent. In contrast to the pairwise entanglement, two-site quantum discord is effectively long-range in the critical regimes where it decays algebraically with the distance between pairs. We also show that the thermal quantum discord between neighbor spins possesses strong distinctive behavior at the critical point that can be seen at finite temperature and, therefore, spotlights the critical point while the entanglement fails in this task.