Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles
Masudul Haque, Paul A. McClarty, Ivan M. Khaymovich
Abstract
Eigenstates of local many-body interacting systems that are far from spectral edges are thought to be ergodic and close to being random states. This is consistent with the eigenstate thermalization hypothesis and volume-law scaling of entanglement. We point out that systematic departures from complete randomness are generically present in midspectrum eigenstates, and focus on the departure of the entanglement entropy from the random-state prediction. We show that the departure is (partly) due to spatial correlations and due to orthogonality to the eigenstates at the spectral edge, which imposes structure on the midspectrum eigenstates.
Topics & Concepts
RandomnessQuantum entanglementEigenvalues and eigenvectorsScalingStatistical physicsErgodic theoryChaoticPhysicsOrthogonalityEntropy (arrow of time)Stationary ergodic processMathematicsRandom matrixFocus (optics)Quantum mechanicsGaussianQuantum chaosThermalisationErgodicityPoint (geometry)Deterministic system (philosophy)Spectrum (functional analysis)Chaotic systemsQuantumStochastic processSpectral propertiesMultipartite entanglementSquashed entanglementQuantum many-body systemsQuantum chaos and dynamical systemsCold Atom Physics and Bose-Einstein Condensates