Broken unitary picture of dynamics in quantum many-body scars

Abstract

Quantum many-body scars (QMBSs) are a novel paradigm for the violation of the eigenstate thermalization hypothesis - Hamiltonians of these systems exhibit mid-spectrum eigenstates that are equidistant in energy and which possess low entanglement and evade thermalization for long times. We present a novel approach to understanding the anomalous dynamical behavior in these systems. Specifically, we postulate that QMBS Hamiltonians H can generically be partitioned into a set of terms Oa which do not commute over the entire Hilbert space, but commute to all orders within the subspace of scar states. All states in the scar subspace thus evolve according to a "broken unitary"Us(t)=Πae-iOat, where H=ΣaOa, which provides a simple interpretation of the anomalous dynamical features exhibited by quantum scars; they evolve in time according to a simpler unitary operator allowing for revivals. It is found that the observed dynamical decoupling is often a direct consequence of simple local conditions, which when satisfied lead to recurring aspects of QMBSs, including equidistant eigenvalues, many-body revivals, and sub-volume-law entanglement entropy. Two classes of scar models emerge in this picture - those with a finite set of Oa, as pertaining of, for instance, scars in the AKLT model, and those with an extensive set of such operators, such as eta pairing scar states in the Hubbard model. Besides discussing how many well-known scar models fit into the above picture, we show how the broken unitary formalism captures many known scar construction methods, known in the literature and generalizes others such as quasiparticles matrix product state (MPS) based methods, and the Shiraishi-Mori approach.