IQIM Postdoctoral and Graduate Student Seminar

Abstract: The structure of Hamiltonian eigenstates can be characterized by their entanglement. Ground states of gapped, local Hamiltonians obey an area law in one dimension, meaning that the the entanglement entropy of an interval is independent of its length. In contrast, "infinite temperature" eigenstates -- those in the middle of the spectrum -- are believed to typically exhibit a volume law: the entanglement entropy of an interval is proportional to its length. We construct a family of exactly solvable, gapless Hamiltonians whose eigenstates have properties characteristic of infinite temperature, like volume-law entanglement entropy, across the whole spectrum -- including the ground state. This construction is the first for which the volume law can be proved to hold for all intervals. The construction is a variation of the Feynman-Kitaev clock -- a well-known mapping between quantum circuits and local Hamiltonians -- where the clock register is given periodic boundary conditions. We combine this with a family of exactly solvable Floquet quantum circuits whose eigenstates we prove obey the eigenstate thermalization hypothesis (ETH) at infinite temperature. The eigenstates of the clock Hamiltonian inherit the volume law entanglement of the circuit eigenstates, demonstrating that gapless ground states can essentially be as complicated as infinite temperature states.

Following the talk, lunch will be provided on the lawn outside East Bridge.