William Faugno : Topology in the Many-Body Spectrum: A Spectral Localizer Approach to Quantum Scars

Quantum many-body scars are a striking form of nonthermal behavior in interacting quantum systems, in which atypical highly excited eigenstates violate the eigenstate thermalization hypothesis and can support long-lived coherent dynamics. While there has been substantial progress in understand the origins of QMBS, a general framework for identifying and characterizing such states remains elusive. Topology provides a powerful framework for identifying robust structure in quantum systems, but its application to many-body systems has traditionally focused on gapped ground states, in part because conventional many-body topological invariants require a well-defined spectral gap. Recently, the spectral localizer has provided a powerful approach to characterizing topology and topological protection in single-particle systems without requiring a spectral gap. In this talk, I will review the single-particle spectral localizer and present an extension to interacting many-body systems that allows us to probe topological structure deep in the many-body spectrum. The states identified by this approach exhibit anomalously low entanglement entropy, violate the eigenstate thermalization hypothesis, and support nonthermal dynamics. We therefore propose a connection between the topological structure revealed by the spectral localizer and quantum many-body scars, and identify these states as candidate prethermal scars.