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arXiv:2506.04782 · Physical Review A

Quantum correlations versus spin magnitude: Transition to the classical limit

Mikhail A. Yurischev, E. I. Kuznetsova, Saeed Haddadi

Published Sep 3, 2025• 2 citations
arXivHTMLPDF

Abstract

Quantum-classical transitions have long attracted much attention. We study such transitions in quantum spin-($j$,1/2) systems at thermal equilibrium. Unlike previous work [Phys. Rev. A 73, 064302 (2006)], we find that the threshold temperature of quantum entanglement decreases with increasing spin $j$ and completely disappears in the limit $j\ensuremath{\rightarrow}\ensuremath{\infty}$. In the ground state of systems with highly symmetric interactions, the discord-type quantum correlations can exist even for arbitrarily large spin. Such correlations turn out to be unstable and are destroyed by small perturbations that violate the symmetry of the Hamiltonian. The stable quantum correlations gradually degrade as the spin $j$ grows and eventually vanish when the classical limit is reached.

DOI
10.1103/qxtm-gysy

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Quantum-classical transitions have long attracted much attention. We study such transitions in quantum spin-(jjj,1/2) systems at thermal equilibrium. Unlike previous work [Phys. Rev. A 73, 064302 (2006)], we find that the threshold temperature of quantum entanglement decreases with increasing spin jjj and completely disappears in the limit j\ensuremath→\ensuremath∞j\ensuremath{\rightarrow}\ensuremath{\infty}j\ensuremath→\ensuremath∞. In the ground state of systems with highly symmetric interactions, the discord-type quantum correlations can exist even for arbitrarily large spin. Such correlations turn out to be unstable and are destroyed by small perturbations that violate the symmetry of the Hamiltonian. The stable quantum correlations gradually degrade as the spin jjj grows and eventually vanish when the classical limit is reached.
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We investigate the disappearance of discord in 2- and multi-qubit systems subject to decohering influences. We formulate the computation of quantum discord and quantum geometric discord in terms of the generalized Bloch vector, which gives useful insights on the time evolution of quantum coherence for the open system, particularly the comparison of entanglement and discord. We show that the analytical calculation of the global geometric discord is NP-hard in the number of qubits, but a similar statement for global entropic discord is more difficult to prove. We present an efficient numerical method to calculating the quantum discord for a certain important class of multipartite states. In agreement with previous work for 2-qubit cases (Mazzola et al 2010 Phys. Rev. Lett. 104 200401), we find situations in which there is a sudden transition from classical to quantum decoherence characterized by the discord remaining relatively robust (classical decoherence) until a certain point from where it begins to decay quickly whereas the classical correlation decays more slowly (quantum decoherence). However, we find that as the number of qubits increases, the chance of this kind of transition occurring becomes small.
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We investigate the mixed-state entanglement between two spins embedded in the XXZ Heisenberg chain under thermal equilibrium. By deriving an analytical expression for the entanglement of two-spin thermal states and extending this analysis to larger spin chains, we demonstrate that mixed-state entanglement is profoundly shaped by both disorder and temperature. Our results reveal a sharp distinction between many-body localized (MBL) and ergodic phases, with entanglement vanishing above different finite temperature thresholds. Furthermore, by analyzing non-adjacent spins, we uncover an approximate exponential decay of entanglement with separation. This work advances the understanding of the quantum-to-classical transition by linking the entanglement properties of small subsystems to the broader thermal environment, offering a explanation for the absence of entanglement in macroscopic systems. These findings provide critical insights into quantum many-body physics, bridging concepts from thermalization, localization, and quantum information theory.