1:30 pm MCP 201
Entanglement and thermalization in (Interacting) Fermion Systems.
After reviewing the entanglement entropy (EE) area law of many-body ground states and in particular its violation, in this talk we demonstrate explicitly the (widely expected but hard to prove) volume law in typical excited free fermion states via a novel duality relation between ground and excited states. More importantly, we find the reduced density matrix of a small subsystem takes the form of thermal density matrix for such typical states, providing an explicit example of the eigenstate thermalization hypothesis (ETH). Being (trivially) integrable, there do exist atypical free fermion states with low EE, now called many-body scar states, that violate ETH. By representing the occupation pattern of each free fermion eigenstate as a classical binary string, we find that the Kolmogorov complexity of the string correctly captures the scaling behavior of EE of the corresponding eigenstate. This allows us to distinguish typical and atypical eigenstates directly by their intrinsic complexity and quantify the degree of their typicality. We further demonstrate analytically that those atypical states are eliminated by weak two-body interaction between the fermions, which mixes typical and atypical states. Specifically, we show that the probability of having a state with EE satisfying a sub-volume scaling law decreases double exponentially with the system size. Thus, our results provide strong quantitative support for ETH and disappearance of scar states in non-integrable interacting fermion systems.