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arXiv · 2012.06505

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

Angelo Russomanno·Michele Fava·Markus Heyl
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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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BibTeXRIS

Angelo Russomanno, Michele Fava, Markus Heyl. 2020-12-11. Quantum chaos and ensemble inequivalence of quantum long-range Ising chains. https://doi.org/10.1103/physrevb.104.094309

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