Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians

Abstract

To which degree the average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians agrees with that of random pure states is a question that has attracted considerable attention in the recent years. While there is substantial evidence that the leading (volume-law) terms are identical, which and how subleading terms differ between them is less clear. Here we carry out state-of-the-art full exact diagonalization calculations of clean spin-1/2 XYZ and XXZ chains with integrability breaking terms to address this question in the absence and presence of $U(1)$ symmetry, respectively. We first introduce the notion of maximally chaotic regime, for the chain sizes amenable to full exact diagonalization calculations, as the regime in Hamiltonian parameters in which the level spacing ratio, the distribution of eigenstate coefficients, and the entanglement entropy are closest to the random matrix theory predictions. In this regime, we carry out a finite-size scaling analysis of the subleading terms of the average entanglement entropy of midspectrum eigenstates when different fractions $\nu$ of the spectrum are included in the average. We find indications that, for $\nu \to 0$, the magnitude of the negative $O(1)$ correction is only slightly greater than the one predicted for random pure states. For finite $\nu$, following a phenomenological approach, we derive a simple expression that describes the numerically observed $\nu$ dependence of the $O(1)$ deviation from the prediction for random pure states.

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• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
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Cited by in corpus (19)

• Many-Body Localization in the Age of Classical Computing
• Quantifying quantum chaos through microcanonical distributions of entanglement
• Stable many-body localization under random continuous measurements in the no-click limit
• Average pure-state entanglement entropy in spin systems with SU(2) symmetry
• Robust non-ergodicity of ground state in the $\beta$ ensemble
• Non-abelian symmetry-resolved entanglement entropy
• Symmetry breaking in chaotic many-body quantum systems at finite temperature
• Typical entanglement entropy in systems with particle-number conservation
• Subsystem entropy in 2d CFT and KdV ETH
• Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model
• Quantum ergodicity and scrambling in quantum annealers
• Late-time ensembles of quantum states in quantum chaotic systems
• Entanglement patterns of quantum chaotic Hamiltonians with a scalar U(1) charge
• Deviations from random matrix entanglement statistics for kicked quantum chaotic spin-$1/2$ chains
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Deviation from maximal entanglement for mid-spectrum eigenstates of local Hamiltonians
• Average mutual information for random fermionic Gaussian quantum states
• Eigenstate Thermalization Hypothesis and Random Matrix Theory Universality in Few-Body Systems
• Efficient computation of average subsystem Bures distance between fermionic Gaussian states