Infinite temperature at zero energy

Understand

We construct a family of static, geometrically local Hamiltonians that inherit eigenstate properties of periodically-driven (Floquet) systems.

• Our 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.
• Assuming the eigenstate thermalization hypothesis (ETH) holds for the input circuit, our construction yields Hamiltonians whose eigenstates have properties characteristic of infinite temperature, like volume-law entanglement entropy, across the whole spectrum -- including the ground state.
• We then construct a family of exactly solvable Floquet quantum circuits whose eigenstates are shown to obey the ETH at infinite temperature.