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We study subsystem entropies in 2d CFTs for subsystems constituting a finite fraction of the full system. We focus on the extensive contribution, which scales linearly with the subsystem size in the thermodynamic limit. We employ the so-called diagonal approximation to evaluate subsystem entropy for chaotic CFTs in the thermal state (canonical ensemble), the microcanonical ensemble, and in a primary state, matching previously known results. We then proceed to find analytic expressions for the subsystem entropy at leading order in , when the global CFT state is the KdV-generalized Gibbs ensemble or the KdV-microcanonical ensemble. Previous studies of primary eigenstates have shown that, akin to the fixed-area states in AdS/CFT, the corresponding subsystem entanglement spectrum is flat. This behavior is seemingly in sharp contradiction with that of the thermal (microcanonical) state, and thus in apparent contradiction with the subsystem eigenstate thermalization hypothesis (ETH). In this paper, we resolve this issue by comparing the primary state with the KdV-(micro)canonical ensemble. We show that the results are consistent with the KdV-generalized version of the subsystem ETH, in which local properties of quantum eigenstates are governed by their values of conserved KdV charges. Our paper solidifies evidence for the KdV-generalized ETH in 2d CFTs and emphasizes Rényi entropy as a sensitive probe of the reduced-density matrix.
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Chaos and Thermalization in the Spin-Boson Dicke Model
We present a detailed analysis of the connection between chaos and the onset of thermalization in the spin-boson Dicke model. This system has a well-defined classical limit with two degrees of freedom, and it presents both regular and chaotic regions. Our studies of the eigenstate expectation values and the distributions of the off-diagonal elements of the number of photons and the number of excited atoms validate the diagonal and off-diagonal eigenstate thermalization hypothesis (ETH) in the chaotic region, thus ensuring thermalization. The validity of the ETH reflects the chaotic structure of the eigenstates, which we corroborate using the von Neumann entanglement entropy and the Shannon entropy. Our results for the Shannon entropy also make evident the advantages of the so-called “efficient basis” over the widespread employed Fock basis when investigating the unbounded spectrum of the Dicke model. The efficient basis gives us access to a larger number of converged states than what can be reached with the Fock basis.
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- Award ID(s):
- 1936006
- PAR ID:
- 10401511
- Date Published:
- Journal Name:
- Entropy
- Volume:
- 25
- Issue:
- 1
- ISSN:
- 1099-4300
- Page Range / eLocation ID:
- 8
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/e25010008
