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## Unconventional Symmetries from Commutant Algebras

### Sanjay Moudgalya (Caltech)

#### Special time: 3pM!

Zoom seminar:

https://cnrs.zoom.us/j/98434226211?pwd=dGJHSlgrNDNhbDcyUE1KdzBSQjc1Zz09

Meeting ID: 984 3422 6211

Passcode: RbqTd5

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.

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