Criticality, factorization and long-range correlations in the anisotropic XY-model

Abstract

We study the long-range quantum correlations in the anisotropic XY-model. By first examining the thermodynamic limit we show that employing the quantum discord as a figure of merit allows one to capture the main features of the model at zero temperature. Further, by considering suitably large site separations we find that these correlations obey a simple scaling behavior for finite temperatures, allowing for efficient estimation of the critical point. We also address ground-state factorization of this model by explicitly considering finite size systems, showing its relation to the energy spectrum and explaining the persistence of the phenomenon at finite temperatures. Finally, we compute the fidelity between finite and infinite systems in order to show that remarkably small system sizes can closely approximate the thermodynamic limit.

8 pages, 8 figures. Close to published version

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• Diagnosing Quantum Phases Using Long-Range Two-Site Quantum Resource Behaviors
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• Generalized Phase-Space Techniques to Explore Quantum Phase Transitions in Critical Quantum Spin Systems
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• Ground state separability and criticality in interacting many-particle systems
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