Level statistics detect generalized symmetries

• URL: http://arxiv.org/abs/2406.03983v1
• Date: Thu, 6 Jun 2024 11:54:28 GMT
• Title: Level statistics detect generalized symmetries
• Authors: Nicholas O'Dea,
• Abstract summary: Level statistics are a useful probe for detecting symmetries and distinguishing integrable and non-integrable systems. I consider non-invertible symmetries through the example of Kramers-Wannier duality at an Ising critical point. I discovered via level statistics a $q$-deformed generalization of inversion that is interesting in its own right and that may protect $q$-deformed SPT phases.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Level statistics are a useful probe for detecting symmetries and distinguishing integrable and non-integrable systems. I show by way of several examples that level statistics detect the presence of generalized symmetries that go beyond conventional lattice symmetries and internal symmetries. I consider non-invertible symmetries through the example of Kramers-Wannier duality at an Ising critical point, symmetries with nonlocal generators through the example of a spin-$1$ anisotropic Heisenberg chain, and $q$-deformed symmetries through an example closely related to recent work on $q$-deformed SPT phases. In each case, conventional level statistics detect the generalized symmetries, and these symmetries must be resolved before seeing characteristic level repulsion in non-integrable systems. For the $q$-deformed symmetry, I discovered via level statistics a $q$-deformed generalization of inversion that is interesting in its own right and that may protect $q$-deformed SPT phases.

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