Description
Symmetries as Commutant Algebras
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 physical phenomena, the recent discoveries of weak ergodicity breaking 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. This leads to a generalization of the conventional notion of symmetry and explains weak ergodicity breaking in terms of unconventional non-local symmetries. In addition, it reveals a novel interpretation of symmetries as ground states of local superoperators, leading to insights on the nature of symmetries realizable in systems with locality.
Title: Symmetries as Commutant Algebras
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 physical phenomena, the recent discoveries of weak ergodicity breaking 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. This leads to a generalization of the conventional notion of symmetry and explains weak ergodicity breaking in terms of unconventional non-local symmetries. In addition, it reveals a novel interpretation of symmetries as ground states of local superoperators, leading to insights on the nature of symmetries realizable in systems with locality.
References:
https://arxiv.org/abs/2108.10324
https://arxiv.org/abs/2209.03370
