Average pure-state entanglement entropy in spin systems with SU(2) symmetry

Abstract

We study the effect that the SU(2) symmetry, and the rich Hilbert space structure that it generates in lattice spin systems, has on the average entanglement entropy of highly excited eigenstates of local Hamiltonians and of random pure states. Focusing on the zero total magnetization sector ($J_z=0$) for different fixed total spin $J$, we argue that the average entanglement entropy of highly excited eigenstates of quantum-chaotic Hamiltonians and of random pure states has a leading volume-law term whose coefficient $s_A$ depends on the spin density $j=J/(\mathfrak{j}L)$, with $s_A(j\to 0)=\ln (2\mathfrak{j}+1)$ and $s_A(j\to 1)=0$, where $\mathfrak{j}$ is the microscopic spin. We provide numerical evidence that $s_A$ is smaller in highly excited eigenstates of integrable interacting Hamiltonians, which lends support to the expectation that the average eigenstate entanglement entropy can be used as a diagnostic of quantum chaos and integrability for Hamiltonians with non-Abelian symmetries. In the context of Hamiltonian eigenstates we consider spins $\mathfrak{j}=\frac{1}{2}$ and $1$, while for our calculations based on random pure states we focus on the spin $\mathfrak{j}=\frac{1}{2}$ case.

16 pages, 8 figures, as published

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• Quantum Many-Body Scars: A Quasiparticle Perspective
• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
• Symmetry-resolved Page curves
• Non-Abelian eigenstate thermalization hypothesis
• Non-Abelian symmetry can increase entanglement entropy
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• Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians
• Eigenstate thermalization hypothesis in two-dimensional XXZ model with or without SU(2) symmetry

Cited by in corpus (13)

• Highly entangled stationary states from strong symmetries
• 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
• Non-Abelian entanglement asymmetry in random states
• Subsystem entropy in 2d CFT and KdV ETH
• Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model
• Eigenstate thermalization in spin-$\frac{1}{2}$ systems with SU(2) symmetry
• Entanglement patterns of quantum chaotic Hamiltonians with a scalar U(1) charge
• Onset of Quantum Chaos and Ergodicity in Spin Systems with Highly Degenerate Hilbert Spaces
• Disorder-Free Localization and Fragmentation in a Non-Abelian Lattice Gauge Theory
• Average mutual information for random fermionic Gaussian quantum states
• Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport