Two classes of quantum spin systems that are gapped on any bounded-degree graph
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912608713441280 |
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| author | Hunter-Jones, Nicholas Lemm, Marius |
| author_facet | Hunter-Jones, Nicholas Lemm, Marius |
| contents | We study translation-invariant quantum spin Hamiltonians on general graphs with non-commuting interactions either given by (i) a random rank-$1$ projection or (ii) Haar projectors. For (i), we prove that the Hamiltonian is gapped on any bounded-degree graph with high probability at large local dimension. For (ii), we obtain a gap for sufficiently large local dimension. Our results provide examples where the folklore belief that typical translation-invariant Hamiltonians are gapped can be proved, which extends a result by Bravyi and Gosset from 1D qubit chains with rank-$1$ interactions to general bounded-degree graphs. We derive the gaps by analytically verifying generalized Knabe-type finite-size criteria that apply to any bounded-degree graph. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_22438 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two classes of quantum spin systems that are gapped on any bounded-degree graph Hunter-Jones, Nicholas Lemm, Marius Quantum Physics Mathematical Physics We study translation-invariant quantum spin Hamiltonians on general graphs with non-commuting interactions either given by (i) a random rank-$1$ projection or (ii) Haar projectors. For (i), we prove that the Hamiltonian is gapped on any bounded-degree graph with high probability at large local dimension. For (ii), we obtain a gap for sufficiently large local dimension. Our results provide examples where the folklore belief that typical translation-invariant Hamiltonians are gapped can be proved, which extends a result by Bravyi and Gosset from 1D qubit chains with rank-$1$ interactions to general bounded-degree graphs. We derive the gaps by analytically verifying generalized Knabe-type finite-size criteria that apply to any bounded-degree graph. |
| title | Two classes of quantum spin systems that are gapped on any bounded-degree graph |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2509.22438 |