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arXiv:2405.16974 · Physical Review A

Inherent quantum resources in stationary spin chains

Marcin Płodzień, Jan Chwedeńczuk, Maciej Lewenstein

Published Jan 9, 2025• 5 citations
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Abstract

The standard way to generate many-body quantum correlations is via a dynamical protocol: an initial product state is transformed by interactions that generate nonclassical correlations at later times. Here, we show that many-body Bell correlations are inherently present in the eigenstates of a variety of spin-1/2 chains. In particular, we show that the eigenstates and thermal states of the collective Lipkin-Meshkov-Glick model possess many-body Bell correlations. We demonstrate that the Bell correlations present in the eigenstates of the Lipkin-Meshkov-Glick model can take on quantized values that change discontinuously with variations in the total magnetization. Finally, we show that these many-body Bell correlations persist even in the presence of both diagonal and off-diagonal disorder.

DOI
10.1103/physreva.111.012417

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The standard way to generate many-body quantum correlations is via a dynamical protocol: an initial product state is transformed by interactions that generate nonclassical correlations at later times. Here, we show that many-body Bell correlations are inherently present in the eigenstates of a variety of spin-1/2 chains. In particular, we show that the eigenstates and thermal states of the collective Lipkin-Meshkov-Glick model possess many-body Bell correlations. We demonstrate that the Bell correlations present in the eigenstates of the Lipkin-Meshkov-Glick model can take on quantized values that change discontinuously with variations in the total magnetization. Finally, we show that these many-body Bell correlations persist even in the presence of both diagonal and off-diagonal disorder.
Dynamical generation of strong and scalable quantum resources, like many-body entanglement and Bell correlations, in spin- 1/2 chains is possible with all-to-all interactions, either for constant interaction strength realizing one-axis twisting protocol or for power-law decaying potentials. We show, however, that such quantum resources can also be dynamically generated with a finite range of interactions. We identify a threshold range and indicate a threshold time when scalable quantum correlations appear. Finally, we show that the certification of generated states is accessible in modern quantum simulator platforms. Published by the American Physical Society 2024
We study the evolution and persistence of quantum and classical correlations between spatially separated sites in the disordered XXZ spin chain in its ergodic and many-body-localized phases using exact diagonalization and matrix product state simulations.We show that in the many-body-localized phase, quantum entanglement survives in long-time unitary dynamics of the system, even though it is more fragile than the classical correlations.We study the dependence of the residual entanglement and correlations on the system size and on the disorder strength.Finally, we demonstrate the robustness of entanglement and correlations with respect to local dissipation in the bulk of the system.
Bell correlations are among the most exotic of the phenomena through which quantum mechanics manifests itself. Their presence signals that the system may violate the postulates of local realism---conjectures once thought to be to be a non-negotiable property of the physical world. The importance of Bell correlations from this fundamental point of view is even further clarified by their applications, ranging from quantum cryptography to quantum metrology and quantum computing. It is therefore of growing interest to characterize the ``Bell content'' of complex, scalable many-body systems. Here, we perform a detailed analysis of the character and strength of many-body Bell correlations in interacting multiqubit systems with particle exchange symmetry. Such a configuration can be described by an effective Schr\"odinger-like equation, which allows precise analytical predictions. We show that in the vicinity of the quantum critical point, these correlations quickly become so strong that only a fraction of the qubits remain uncorrelated. We also identify the threshold temperature above which thermal fluctuations destroy Bell correlations. We hope that the approach presented here, due to its universality, will be useful for upcoming research on genuinely nonclassical Bell-correlated complex systems.
Controlling the dynamics of quantum many-body systems is crucial for developing quantum technologies. This work demonstrates that counterdiabatic (CD) driving provides a powerful tool for steering collective spin systems along entangled trajectories for a long time. In particular, CD driving leads to approximate stroboscopic freezing and eternal entanglement oscillations for a large class of initial states in the periodically driven Lipkin-Meshkov-Glick model. Intriguingly, CD driving generates spin squeezing and its associated metrologically useful multipartite entanglement at the mid-point of every drive cycle, when the system is initially prepared in a fully x-polarized state. The CD driving induced nonergodic dynamics is accompanied by a decrease in the average eigenstate entanglement and inverse participation ratio, thereby signaling greater eigenstate localization. Our work opens a new route to evade Floquet heating and control entanglement generation in collective spin systems.
In this paper we theoretically report an unconventional quantum phase transition of a simple Lipkin–Meshkov–Glick model: an interacting collective spin system without external magnetic field. It is shown that this model with integer-spin can exhibit a first-order quantum phase transition between different disordered phases, and more intriguingly, possesses a hidden supersymmetry at the critical point. However, for half-integer spin we predict another first-order quantum phase transition between two different long-range-ordered phases with a vanishing energy gap, which is induced by the destructive topological quantum interference between the intanton and anti-instanton tunneling paths and accompanies spontaneously breaking of supersymmetry at the same critical point. We also show that, when the total spin-value varies from half-integer to integer this model can exhibit an abrupt variation of Berry phase from π to zero.
Bell correlations are among the most exotic phenomena through which quantum mechanics manifests itself. Their presence signals that the system can violate the postulates of local realism, once believed to be the nonnegotiable property of the physical world. The importance of Bell correlations from this fundamental point of view is even straightened by their applications -- ranging from quantum cryptography through quantum metrology to quantum computing. Hence it is of growing interest to characterize the ``Bell content'' of complex, scalable many-body systems. Here we perform the detailed analysis of the character and strength of many-body Bell correlations in interacting multi-qubit systems with particle-exchange symmetry. Such configuration can be mapped onto an effective Schrödinger-like equation, which allows for precise analytical predictions. We show that in the vicinity of the quantum critical point, these correlations quickly become so strong that only a fraction of qubits remains uncorrelated. We also identify the threshold temperature, which, once overpassed, empowers thermal fluctuations that destroy Bell correlations in the system. We hope that the approach presented here, due to its universality, could be useful for the upcoming research on genuinely nonclassical Bell-correlated complex systems.