Generalized Gibbs Ensemble of 2d CFTs at large central charge in the thermodynamic limit

We discuss partition function of 2d CFTs decorated by higher qKdV charges in the thermodynamic limit when the size of the spatial circle goes to infinity. In this limit the saddle point approximation is exact and at infinite central charge generalized partition function can be calculated explicitly. We show that leading 1/c corrections to free energy can be reformulated as a sum over Young tableaux which we calculate for the first two qKdV charges. Next, we compare generalized ensemble with the "eigenstate ensemble" that consists of a single primary state. At infinite central charge the ensembles match at the level of expectation values of local operators for any values of qKdV fugacities. When the central charge is large but finite, for any values of the fugacities the aforementioned ensembles are distinguishable.Comment: 23 page

Universality of fast quenches from the conformal perturbation theory

We consider global quantum quenches, a protocol when a continuous field theoretic system in the ground state is driven by a homogeneous time-dependent external interaction. When the typical inverse time scale of the interaction is much larger than all relevant scales except for the UV-cutoff the system's response exhibits universal scaling behavior. We provide both qualitative and quantitative explanations of this universality and argue that physics of the response during and shortly after the quench is governed by the conformal perturbation theory around the UV fixed point. We proceed to calculate the response of one and two-point correlation functions confirming and generalizing universal scalings found previously. Finally, we discuss late time behavior after the quench and argue that all local quantities will equilibrate to their thermal values specified by an excess energy acquired by the system during the quench.Comment: published version, refs added, minor typos corrected, 38 pages, no fgiure

Bound on Eigenstate Thermalization from Transport

We show that presence of transport imposes constraints on matrix elements entering the Eigenstate Thermalization Hypothesis (ETH) ansatz and require them to be correlated. It is generally assumed that the ETH ansatz reduces to Random Matrix Theory (RMT) below the Thouless energy scale. We show this conventional picture is not self-consistent. We prove that the energy scale at which ETH ansatz reduces to RMT has to be parametrically smaller than the inverse timescale of the slowest thermalization mode present in the system. In particular it has to be parametrically smaller than the Thouless energy. Our results indicate there is a new scale relevant for thermalization dynamics

Universality of Quantum Information in Chaotic CFTs

We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute the reduced density matrix of a ball-shaped subsystem of finite size in the infinite volume limit when the full system is an energy eigenstate. This reduced density matrix is close in trace distance to a density matrix, to which we refer as the ETH density matrix, that is independent of all the details of an eigenstate except its energy and charges under global symmetries. In two dimensions, the ETH density matrix is universal for all theories with the same value of central charge. We argue that the ETH density matrix is close in trace distance to the reduced density matrix of the (micro)canonical ensemble. We support the argument in higher dimensions by comparing the Von Neumann entropy of the ETH density matrix with the entropy of a black hole in holographic systems in the low temperature limit. Finally, we generalize our analysis to the coherent states with energy density that varies slowly in space, and show that locally such states are well described by the ETH density matrix.Comment: 43 page