Kavli Affiliate: Huajia Wang
| First 5 Authors: Liangyu Chen, Anatoly Dymarsky, Jia Tian, Huajia Wang,
| Summary:
We study subsystem entropy 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 the
chaotic CFTs in thermal state (canonical ensemble), 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 $c$,
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 fixed-area states in AdS/CFT, corresponding subsystem
entanglement spectrum is flat. This behavior is seemingly in sharp
contradiction with the one for the thermal (microcanonical) state, and thus in
apparent contradiction with the subsystem Eigenstate Thermalization Hypothesis
(ETH). In this work, 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
work solidifies evidence for the KdV-generalized ETH in 2d CFTs and emphasizes
Renyi entropy as a sensitive probe of the reduced-density matrix.
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