Structure of chaotic eigenstates and their entanglement entropy

Murthy, Chaitanya; Srednicki, Mark

doi:10.1103/PhysRevE.100.022131

Structure of chaotic eigenstates and their entanglement entropy

Jun 10, 2019

8 pages

Published in:

Phys.Rev.E 100 (2019) 2, 022131

Published: Aug 23, 2019

e-Print:

1906.04295 [cond-mat.stat-mech]

DOI:

10.1103/PhysRevE.100.022131 (publication)

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Abstract: (APS)

We consider a chaotic many-body system (i.e., one that satisfies the eigenstate thermalization hypothesis) that is split into two subsystems, with an interaction along their mutual boundary, and study the entanglement properties of an energy eigenstate with nonzero energy density. When the two subsystems have nearly equal volumes, we find a universal correction to the entanglement entropy that is proportional to the square root of the system's heat capacity (or a sum of capacities, if there are conserved quantities in addition to energy). This phenomenon was first noted by Vidmar and Rigol in a specific system; our analysis shows that it is generic, and expresses it in terms of thermodynamic properties of the system. Our conclusions are based on a refined version of a model of a chaotic eigenstate originally due to Deutsch, and analyzed more recently by Lu and Grover.

Note:

8 pages, 1 figure. Changed title to match published version, fixed minor typos and added a footnote

Statistical Physics
entropy: entanglement
chaos
many-body problem
energy eigenstate
thermodynamical
numerical calculations

References(18)

Figures(1)

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