(N)On Thermality of CFT Eigenstates
Sridip Pal (University of California, San Diego)
The Eigenstate Thermalization Hypothesis (ETH) provides a way to understand how and when an isolated quantum mechanical system can be approximated by a thermal density matrix. We find a class of operator in (1+1)-d conformal field theories, consisting of quasi-primaries of the identity module, which satisfy the hypothesis only at the leading order in large central charge. In the context of subsystem ETH i.e thermalization of subsystem, this plays a role in the deviation of the reduced density matrix, corresponding to a finite energy density eigenstate from its hypothesized thermal approximation. The universal deviation in terms of the square of the trace-square distance goes as the 8th power of the subsystem fraction and is suppressed by powers of inverse central charge. Furthermore, the non-universal deviations from subsystem ETH are found to be proportional to the heavy-light-heavy structure constants which are typically exponentially suppressed in √ h/c .