Quantum chaos and ensemble inequivalence of quantum long-range Ising chains

• URL: http://arxiv.org/abs/2012.06505v3
• Date: Wed, 29 Sep 2021 16:25:41 GMT
• Title: Quantum chaos and ensemble inequivalence of quantum long-range Ising chains
• Authors: Angelo Russomanno, Michele Fava, and Markus Heyl
• Abstract summary: We use large-scale exact diagonalization to study the quantum Ising chain in a transverse field with long-range powerlaw interactions with exponents. Our findings suggest that a small fraction of energies could persist at low energies for $alpha1$ even for large $N$, giving rise to ensemble inequivalence.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We use large-scale exact diagonalization to study the quantum Ising chain in a transverse field with long-range power-law interactions decaying with exponent $\alpha$. We numerically study various probes for quantum chaos and eigenstate thermalization {on} the level of eigenvalues and eigenstates. The level-spacing statistics yields a clear sign towards a Wigner-Dyson distribution and therefore towards quantum chaos across all values of $\alpha>0$. Yet, for $\alpha<1$ we find that the microcanonical entropy is nonconvex. This is due to the fact that the spectrum is organized in energetically separated multiplets for $\alpha<1$. While quantum chaotic behaviour develops within the individual multiplets, many multiplets don't overlap and don't mix with each other, as we analytically and numerically argue. Our findings suggest that a small fraction of the multiplets could persist at low energies for $\alpha\ll 1$ even for large $N$, giving rise to ensemble inequivalence.

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