Quantum semniar: Sanjay Moudgalya (Technical University of Munich)

Title: Symmetries as Ground States of Local Hamiltonians

Abstract: The study of symmetry lies at the heart of various parts of physics. However, the symmetries conventionally studied in a lot of the literature are mostly restricted to either on-site unitary symmetries or lattice symmetries. While such symmetries are sufficient to explain several textbook physical phenomena, the recent discovery of dynamical phenomena such as Hilbert space fragmentation and quantum many-body scars have called for a reconsideration of the definition of symmetry in quantum many-body physics. In this talk, I will discuss a general mathematical framework to define symmetries based on so-called commutant algebras, which generalizes the conventional notion of symmetry and explains these novel phenomena in terms of unconventional non-local symmetries. In addition, it reveals a novel characterization of symmetries as frustration-free ground states of local superoperator Hamiltonians, which leads to insights on the nature of symmetries realizable in systems with locality. Further, the low-energy excitations of this superoperator are related to hydrodynamic modes of the corresponding symmetries, and this unifies the understanding of many kinds of symmetries and their associated hydrodynamic modes into a single framework.

Reference: https://arxiv.org/abs/2309.15167

Refreshments at 10:15, followed by the talk from 10:30-12.00.