Quantum many-body scars, connection to Floquet automata, and ‘broken unitary’ dynamics

JQI Special Seminar

Kartiek Agarwal (McGill University)
Friday, January 13, 2023 - 11:00am
PSC 2136 and Virtual Via Zoom

Quantum Many-Body scars represent a new paradigm of breaking eigenstate thermalization hypothesis—a vanishing number of states in the spectrum exhibit area law entanglement while being dispersed at equally spaced energies throughout a spectrum of volume-law entangled states. This is in stark contrast to many-body localization, where all eigenstates are area-law entangled, or a thermalizing system, where states are volume law entangled. Despite the fact that very few states exhibit such low entanglement, they have a remarkable effect on the dynamics of the system. In particular, when the system is prepared in certain initial states, it refuses to thermalize up to extremely long times, exhibiting periodic revivals of the initial state. Such physics was first discovered in the PXP model, but appears to be present in the AKLT model, generalizations of the Hubbard model, among others. In this talk, I will discuss how one can understand the presence of such low-entanglement mid-spectrum states by relating these strongly interacting models with non-trivial dynamics, to very simple Floquet systems governed by classical automaton dynamics. This connection helps us understand the emergence of non-thermalizing subspaces in this system due to the formation of certain non-local integrals of motion, and allows one to extract an approximate timescale for the decay of the many-body recurrences. We also discuss how these ideas can be leveraged to realize new Hamiltonians that exhibit quantum scars, and for which the timescale of the decay recurrences can be tuned from fairly short times to infinite. We further generalize these ideas using a novel ‘broken unitary’ interpretation of quantum scar dynamics.