Entanglement patterns of quantum chaotic Hamiltonians with a scalar U(1) charge
arXiv:2403.10600 · doi:10.1103/xxlq-d1sw
Abstract
Our current understanding of quantum chaos in many-body quantum systems hinges on the random matrix theory(RMT) behavior of eigenstates and their energy level statistics. Although RMT has been remarkably successful in describing `coarse' features of many-body quantum Hamiltonians in chaotic regimes, such as the Wigner-Dyson level spacing statistics or the volume-law behavior of eigenstate entanglement entropy, it remains a challenge to describe their `finer' features, particularly those arising from spatial locality. Here, we show that we can accurately describe the statistical behavior of eigenstate ensembles in many-body Hamiltonians by using pure random states with physical constraints that capture the essential features of the Hamiltonian, specifically spatial locality and symmetries. We demonstrate our approach on local spin Hamiltonians with a scalar U(1) charge. By constructing ensembles of constrained random states that account for two commuting scalar charges playing the role of energy and magnetization, we describe the patterns of entanglement of mid-spectrum eigenstates beyond their average volume-law behavior, including corrections and fluctuations, analytically and numerically. When defining the correspondence between quantum chaotic eigenstates in many-body Hamiltonians and RMT ensembles, our work highlights the important role played by spatial locality in describing universal features beyond the volume-law behavior.
arXiv comment6+6 pages (3+2 figures)
References in corpus (48)
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Many body localization and thermalization in quantum statistical mechanics
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Localization of interacting fermions at high temperature
- Average Entropy of a Subsystem
- Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Eigenstate Thermalization Hypothesis
- The approach to thermal equilibrium in quantized chaotic systems
- Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
- Solution of a minimal model for many-body quantum chaos
- Does a single eigenstate encode the full Hamiltonian?
- Thermalization near integrability in a dipolar quantum Newton's cradle
- Spectral statistics in spatially extended chaotic quantum many-body systems
- Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
- Onset of Random Matrix Behavior in Scrambling Systems
- Subsystem ETH
- Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
- The Eigenstate Thermalization Hypothesis and Out of Time Order Correlators
- Spectral statistics and many-body quantum chaos with conserved charge
- Determining a local Hamiltonian from a single eigenstate
- Statistical distribution of quantum entanglement for a random bipartite state
- Phase Transitions in the Distribution of Bipartite Entanglement of a Random Pure State
- Renyi Entropy of Chaotic Eigenstates
- Joint probability densities of level spacing ratios in random matrices
- Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies
- Local pairing of Feynman histories in many-body Floquet models
- Structure of chaotic eigenstates and their entanglement entropy
- Eigenstate Correlations, Thermalization and the Butterfly Effect
- Universal eigenstate entanglement of chaotic local Hamiltonians
- Typical entanglement entropy in the presence of a center: Page curve and its variance
- The Page Curve for Fermionic Gaussian States
- Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
- Random pure states: quantifying bipartite entanglement beyond the linear statistics
- Bound on Eigenstate Thermalization from Transport
- Out-of-time-order correlations and the fine structure of eigenstate thermalisation
- Non-Abelian eigenstate thermalization hypothesis
- Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
- Non-Abelian symmetry can increase entanglement entropy
- A Proof of Vivo-Pato-Oshanin's Conjecture on the Fluctuation of von Neumann Entropy
- Entanglement in random pure states: Spectral density and average von Neumann entropy
- Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians
- Typical entanglement for Gaussian states
- Quantifying quantum chaos through microcanonical distributions of entanglement
- Average pure-state entanglement entropy in spin systems with SU(2) symmetry
- Typical entanglement entropy in systems with particle-number conservation
- Deviation from maximal entanglement for mid-spectrum eigenstates of local Hamiltonians