Onsager's scars in non-integrable spin chains

· Date: August 7(Fri.), 2020

· Place: Online (ZOOM)

· Website: https://www.apctp.org/plan.php/TQM4

· Overview

: The algebraic construction of the eigenstates of a Hamiltonian (or other conserved charges) is at the heart of quantum integrable models. Usually, this fails miserably in non-integrable models. However, recent studies on quantum many-body scar (QMBS) states have revealed a class of non-integrable models in which towers of exact eigenstates are built up by repeatedly acting with a certain ``creation operator" on a simple (low-entanglement) state. Examples of such models include the Affleck-Kennedy-Lieb-Tasaki and the spin-1 XY models. The eigenstates constructed this way have low entanglement even though their energies are in the middle of the spectrum, and thus violate the strong Eigenstate Thermalization Hypothesis (ETH). In this talk, I will show that an infinite sequence of non-integrable models with QMBS can be constructed using the so-called Onsager algebra. Interestingly, this construction allows for the Hamiltonian to be spatially inhomogeneous. I will also show that the dynamics from a special class of initial states exhibits persistent many-body revivals. If time permits, I will talk about another algebraic approach to construct a class of models with QMBS.

· Invited Speakers: Hosho Katsura (The University of Tokyo)