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Fragmentation-induced localization and boundary charges in dimensions two and above
by Julius Lehmann, Pablo Sala de Torres-Solanot, Frank Pollmann, Tibor Rakovszky
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Submission summary
| Authors (as registered SciPost users): | Julius Lehmann · Tibor Rakovszky · Pablo Sala de Torres-Solanot |
| Submission information | |
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| Preprint Link: | scipost_202209_00033v4 (pdf) |
| Date accepted: | 2023-04-03 |
| Date submitted: | 2023-02-22 17:43 |
| Submitted by: | Sala de Torres-Solanot, Pablo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We study higher dimensional models with symmetric correlated hoppings, which generalize a one-dimensional model introduced in the context of dipole-conserving dynamics. We prove rigorously that whenever the local configuration space takes its smallest non-trivial value, these models exhibit localized behavior due to fragmentation, in any dimension. For the same class of models, we then construct a hierarchy of conserved quantities that are power-law localized at the boundary of the system with increasing powers. Combining these with Mazur's bound, we prove that boundary correlations are infinitely long lived, even when the bulk is not localized. We use our results to construct quantum Hamiltonians that exhibit the analogues of strong zero modes in two and higher dimensions
List of changes
- We have included a new sentence in the second paragraph of page 5: "We have also numerically confirmed that spatial correlations remain localized to a finite region."
- We have corrected "L" as "L^d" whenever necessary in the statement and proof of Theorem 2 in page 10.
- We have eliminated previous appendix B "Strong fragmentation of the configuration space" which had the same content as the current proof of Theorem 2.
Published as SciPost Phys. 14, 140 (2023)