Bipartite Sachdev-Ye Models with Read-Saleur Symmetries
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| Format: | Preprint |
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2024
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| _version_ | 1866914970968522752 |
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| author | Classen-Howes, J. Fendley, P. Pandey, A. Parameswaran, S. A. |
| author_facet | Classen-Howes, J. Fendley, P. Pandey, A. Parameswaran, S. A. |
| contents | We introduce an SU(M)-symmetric disordered bipartite spin model with unusual characteristics. Although superficially similar to the Sachdev-Ye model, it has several markedly different properties for M>2. In particular, it has a large non-trivial nullspace whose dimension grows exponentially with system size. The states in this nullspace are frustration-free, and are ground states when the interactions are ferromagnetic. The exponential growth of the nullspace leads to Hilbert-space fragmentation and a violation of the eigenstate thermalization hypothesis. We demonstrate that the commutant algebra responsible for this fragmentation is a non-trivial subalgebra of the Read-Saleur commutant algebra of certain nearest-neighbour models such as the spin-1 biquadratic spin chain. We also discuss the low-energy behaviour of correlations for the disordered version of this model in the limit of a large number of spins and large M, using techniques similar to those applied to the SY model. We conclude by generalizing the Shiraishi-Mori embedding formalism to non-local models, and apply it to turn some of our nullspace states into quantum many-body scars. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15270 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bipartite Sachdev-Ye Models with Read-Saleur Symmetries Classen-Howes, J. Fendley, P. Pandey, A. Parameswaran, S. A. Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory We introduce an SU(M)-symmetric disordered bipartite spin model with unusual characteristics. Although superficially similar to the Sachdev-Ye model, it has several markedly different properties for M>2. In particular, it has a large non-trivial nullspace whose dimension grows exponentially with system size. The states in this nullspace are frustration-free, and are ground states when the interactions are ferromagnetic. The exponential growth of the nullspace leads to Hilbert-space fragmentation and a violation of the eigenstate thermalization hypothesis. We demonstrate that the commutant algebra responsible for this fragmentation is a non-trivial subalgebra of the Read-Saleur commutant algebra of certain nearest-neighbour models such as the spin-1 biquadratic spin chain. We also discuss the low-energy behaviour of correlations for the disordered version of this model in the limit of a large number of spins and large M, using techniques similar to those applied to the SY model. We conclude by generalizing the Shiraishi-Mori embedding formalism to non-local models, and apply it to turn some of our nullspace states into quantum many-body scars. |
| title | Bipartite Sachdev-Ye Models with Read-Saleur Symmetries |
| topic | Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2403.15270 |