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Quantum Thermodynamics

Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems

arXiv
Authors: Hsin-Hua Lai, Kun Yang

Year

2014

Paper ID

47734

Status

Preprint

Abstract Read

~2 min

Abstract Words

109

Citations

N/A

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.

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  • 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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1409.1224 [2] arXiv https://arxiv.org/abs/1409.1224 [3] Publisher https://arxiv.org/abs/1409.1224

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