Quantum Discord in the Ground and Thermal States of Spin Clusters

TL;DR

This paper investigates quantum discord in symmetric spin clusters, analyzing its behavior in ground and thermal states, and under decoherence, revealing unique properties and phase transition effects in molecular magnets.

Contribution

It provides the first detailed analysis of quantum discord in spin trimers and tetramers, including its dynamics and relation to quantum phase transitions.

Findings

Quantum discord remains finite in the trimer ground state despite zero entanglement.

Quantum discord exhibits discontinuities at quantum phase transition points.

Quantum discord vanishes only at infinite temperature.

Abstract

Quantum discord is a general measure of bipartite quantum correlations with a potential role in quantum information processing tasks. Spin clusters serve as ideal candidates for the implementation of some of the associated protocols. In this paper, we consider a symmetric spin trimer and a tetramer, which describe a number of known molecular magnets, and compute the quantum discord in the ground and thermal states of the clusters. The variations of the quantum discord as a function of anisotropy parameter, magnetic field and temperature are investigated. We obtain a number of interesting results such as a finite value of the quantum discord in the trimer ground state for which the pairwise entanglement is known to be zero, differences in the nature of some of the variations in the ferromagnetic and antiferromagnetic cases and discontinuous jumps in the magnitude of the quantum discord at first order quantum phase transition points. A remarkable feature that is observed is that the quantum discord completely vanishes only in the asymptotic limit of temperature $T\rightarrow\infty$. We further study the dynamics of the quantum discord and the pairwise entanglement at T=0 under the effect of a dephasing channel describing the interaction of the reduced spin cluster state with independent local environments. The QD is found to vanish asymptotically as $t\rightarrow\infty$. In the case of the spin trimer, the pairwise entanglement has a zero value at all times and reaches a zero value in a finite time in the case of the tetramer.