Complexity of thermal states in quantum spin chains

Abstract

We study quantum correlations and complexity of simulation, characterized by quantum mutual information and entanglement entropy in operator space respectively, for thermal states in critical, non-critical and quantum chaotic spin chains. A simple general relation between the two quantities is proposed. We show that in all cases mutual information and entanglement entropy saturate with the system size, whereas as a function of the inverse temperature, we find logarithmic divergences for critical cases and uniform bounds in non-critical cases. A simple efficient quasi-exact method for computation of arbitrary entropy related quantities in thermalized XY spin chains is proposed.

5 pages, 3 eps figures; v2. minor changes, sections added

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Cited by in corpus (49)

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• Genuine quantum correlations in quantum many-body systems: a review of recent progress
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• Entanglement entropy of excited states
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• Quantum information scrambling after a quantum quench
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• Diffusion and operator entanglement spreading
• Generating a state $t$-design by diagonal quantum circuits
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• Dynamics of Fluctuations in Quantum Simple Exclusion Processes
• Signatures of many-body localization in steady states of open quantum systems
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• Quantum many-body systems in thermal equilibrium
• Landauer Current and Mutual Information
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• A solvable model for graph state decoherence dynamics
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• Sample complexity of matrix product states at finite temperature
• Fast Scrambling in Classically Simulable Quantum Circuits