Eigenstate capacity and Page curve in fermionic Gaussian states

Abstract

Capacity of entanglement (CoE), an information-theoretic measure of entanglement, defined as the variance of modular Hamiltonian, is known to capture the deviation from the maximal entanglement. We derive an exact expression for the average eigenstate CoE in fermionic Gaussian states as a finite series, valid for arbitrary bi-partition of the total system. Further, we consider the complex SYK${}_2$ model in the thermodynamic limit and we obtain a closed-form expression of average CoE. In this limit, the variance of the average CoE becomes independent of the system size. Moreover, when the subsystem size is half of the total system, the leading volume-law coefficient approaches a value of ${\pi }^2/8-1$. We identify this as a distinguishing feature between integrable and quantum-chaotic systems. We confirm our analytical results by numerical computations.

arXiv comment12 pages, 6 figures, minor changes, references added, to appear in Phys. Rev. B

References in corpus (58)

• Entanglement in quantum critical phenomena
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Information in Black Hole Radiation
• Calculation of reduced density matrices from correlation functions
• Reduced density matrices and entanglement entropy in free lattice models
• The entropy of Hawking radiation
• Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
• Holographic metals and the fractionalized Fermi liquid
• Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
• Remarks on the notion of quantum integrability
• Does a single eigenstate encode the full Hamiltonian?
• Entanglement entropy and entanglement spectrum of the Kitaev model
• Canonical Thermal Pure Quantum State
• Circuit Complexity in Fermionic Field Theory
• Thermal Pure Quantum States at Finite Temperature
• Average Entropy of a Subsystem
• Circuit complexity for free fermions
• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
• Entanglement and matrix elements of observables in interacting integrable systems
• Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians
• Spread of entanglement in a Sachdev-Ye-Kitaev chain
• Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
• Universality in volume law entanglement of pure quantum states
• Eigenstate thermalization in the Sachdev-Ye-Kitaev model
• Volume Law and Quantum Criticality in the Entanglement Entropy of Excited Eigenstates of the Quantum Ising Model
• Renyi Entropy of Chaotic Eigenstates
• Quantum Entanglement of the Sachdev-Ye-Kitaev Models
• Thermodynamic entropy of a many body energy eigenstate
• Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians
• Structure of chaotic eigenstates and their entanglement entropy
• Probing Hawking radiation through capacity of entanglement
• Aspects of capacity of entanglement
• Universal eigenstate entanglement of chaotic local Hamiltonians
• The Page Curve for Fermionic Gaussian States
• Typical entanglement entropy in the presence of a center: Page curve and its variance
• Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic models
• Eigenstate entanglement in the Sachdev-Ye-Kitaev model
• Replica wormholes and capacity of entanglement
• Entanglement in ground and excited states of gapped fermion systems and their relationship with fermi surface and thermodynamic equilibrium properties
• Entanglement in many-body eigenstates of quantum-chaotic quadratic Hamiltonians
• Entanglement distribution in the Quantum Symmetric Simple Exclusion Process
• Periodically Driven Sachdev-Ye-Kitaev Models
• A Holographic Proof of Rényi Entropic Inequalities
• Subsystem Rényi Entropy of Thermal Ensembles for SYK-like models
• Theory of transformation for the diagonalization of quadratic Hamiltonians
• Eigenstate entanglement: Crossover from the ground state to volume laws
• Eigenstate entanglement entropy in $PT$ invariant non-Hermitian system
• Renyi entanglement entropy of Fermi liquids and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories
• Entanglement Entropy and its Quench Dynamics for Pure States of the Sachdev-Ye-Kitaev model
• Capacity of Entanglement in Local Operators
• Capacity of entanglement in random pure state
• Capacity of entanglement and distribution of density matrix eigenvalues in gapless systems
• Page Curves for General Interacting Systems
• The three-loop QED contributions to the $g-2$ of charged leptons with two internal fermion loops and a class of Kampé de Fériet series
• Spectral Properties of the Jacobi Ensembles via the Coulomb Gas approach
• Entanglement dualities in supersymmetry
• Quantum hypothesis testing in many-body systems

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