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Abstract |
The study of symmetry lies at the heart of various parts of physics. In equilibrium physics, symmetries are
useful in classifying phases of matter and in non-equilibrium physics, they are necessary to understand the
phenomenon of thermalization. Most symmetries conventionally studied in the literature are examples of so-
called on-site unitary symmetries. While such symmetries are sufficient to explain several physical
phenomena, the recent discovery of weak ergodicity breaking in quantum many-body systems, particularly
the phenomena of Hilbert Space Fragmentation and Quantum Many-Body Scars, has called for a
generalization of the notion of symmetry. The conventional theory of thermalization in quantum many-body
systems demands that all states within a given symmetry sector can be connected to each other under the
dynamics of the system. However, quantum many-body systems exhibiting weak ergodicity breaking possess
additional closed subspaces that are dynamically disconnected from the rest of the Hilbert space. These
subspaces cannot be explained in terms of conventional symmetries, which leads to a breakdown of
conventional thermalization in such systems. In this talk, I will discuss a general mathematical framework to
define symmetries based on so-called commutant algebras, which leads to a generalization of the notion of
symmetry beyond the conventional ones. This provides a precise explanation of weak ergodicity breaking in
terms of unconventional non-local symmetries, allows us to cast various different dynamical phenomena in
the literature into a single unified framework, and also opens up several questions on symmetries.
References:
https://arxiv.org/abs/2108.10324
https://arxiv.org/abs/2209.03370
https://arxiv.org/abs/2209.03377 |
