Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems

Abstract

We demonstrate that the entanglement entropy area law for free fermion ground states and the corresponding volume law for highly excited states are related by a position-momentum duality, thus of the same origin. For a typical excited state in the thermodynamic limit, we further show that the reduced density matrix of a subsystem approaches thermal density matrix, provided the subsystem's linear size is small compared to that of the whole system in all directions, a property we dub eigenstate typicality. This provides an explicit example of thermalization via entanglement, and reveals how statistical physics emerges from a single eigenstate by tracing out a large number of degrees of freedom.

4.5 pages, 2 figures

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• Generalized eigenstate typicality in translation-invariant quasifree fermionic models
• Entanglement scaling in fermion chains with a localization-delocalization transition and inhomogeneous modulations
• Assigning Temperatures to Eigenstates
• Free-fermion Page Curve: Canonical Typicality and Dynamical Emergence
• Quantum master equation from the eigenstate thermalization hypothesis
• Scaling at the OTOC Wavefront: free versus chaotic models
• Typical entanglement entropy in systems with particle-number conservation
• Microscopic contributions to the entropy production at all times: From nonequilibrium steady states to global thermalization
• Open-system eigenstate thermalization in a noninteracting integrable model
• Symmetry classification of typical quantum entanglement
• Eigenstate thermalization and disappearance of quantum many-body scar states in interacting fermion systems
• Kolmogorov complexity as intrinsic entropy of a pure state: Perspective from entanglement in free fermion systems
• Entanglement scaling behaviors of free fermions on hyperbolic lattices
• Average Rényi Entanglement Entropy in Gaussian Boson Sampling
• No eigenstate of the critical transverse-field Ising chain satisfies the area law
• Many-body eigenstate thermalization from one-body quantum chaos: emergent arrow of time
• Volume-law entanglement entropy of typical pure quantum states
• Trade-off between diagonal and off-diagonal elements in the eigenstate thermalization hypothesis