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.

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

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• Page curves and typical entanglement in linear optics
• Average capacity of quantum entanglement
• Free-fermion Page Curve: Canonical Typicality and Dynamical Emergence
• Disentangling Interacting Systems with Fermionic Gaussian Circuits: Application to Quantum Impurity Models
• Symmetry classification of typical quantum entanglement
• Evolution of capacity of entanglement and modular entropy in harmonic chains and scalar fields
• Electric potentials and field lines for uniformly-charged tube and cylinder expressed by Appell's hypergeometric function and integration of $Z(u|m)\mathrm{sc}(u|m)$
• Relaxation Fluctuations of Correlation Functions: Spin and Random Matrix Models
• Average Rényi Entanglement Entropy in Gaussian Boson Sampling
• Entanglement capacity of fermionic Gaussian states
• Non-Universality from Conserved Superoperators in Unitary Circuits
• Extended Holographic Rényi Entropy and hyperbolic black hole with scalar hair
• Volume-law entanglement entropy of typical pure quantum states
• The area and volume laws for entanglement of scalar fields in flat and cosmological spacetimes