Lieb-Schultz-Mattis Theorem with Long-Range Interactions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916385778565120 |
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| author | Ma, Ruochen |
| author_facet | Ma, Ruochen |
| contents | We prove the Lieb-Schultz-Mattis theorem in $d$-dimensional spin systems exhibiting $SO(3)$ spin rotation and lattice translation symmetries in the presence of $k-$local interactions decaying as $\sim 1/r^α$ with distance $r$. Two types of Hamiltonians are considered: Type I comprises long-range spin-spin couplings, while Type II features long-range couplings between $SO(3)$ symmetric local operators. For spin-$\frac{1}{2}$ systems, it is shown that Type I cannot have a unique symmetric ground state with a nonzero excitation gap when the interaction decays sufficiently fast, \ie when $α>\max(3d,4d-2)$. For Type II, the condition becomes $α>\max(3d-1,4d-3)$. In $1d$, this ingappability condition is improved to $α>2$ for Type I and $α>0$ for Type II by examining the energy of a state with a uniform $2π$ twist. Notably, in $2d$, a Type II Hamiltonian with van der Waals interaction is subject to the constraint of the theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14949 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lieb-Schultz-Mattis Theorem with Long-Range Interactions Ma, Ruochen Strongly Correlated Electrons Quantum Physics We prove the Lieb-Schultz-Mattis theorem in $d$-dimensional spin systems exhibiting $SO(3)$ spin rotation and lattice translation symmetries in the presence of $k-$local interactions decaying as $\sim 1/r^α$ with distance $r$. Two types of Hamiltonians are considered: Type I comprises long-range spin-spin couplings, while Type II features long-range couplings between $SO(3)$ symmetric local operators. For spin-$\frac{1}{2}$ systems, it is shown that Type I cannot have a unique symmetric ground state with a nonzero excitation gap when the interaction decays sufficiently fast, \ie when $α>\max(3d,4d-2)$. For Type II, the condition becomes $α>\max(3d-1,4d-3)$. In $1d$, this ingappability condition is improved to $α>2$ for Type I and $α>0$ for Type II by examining the energy of a state with a uniform $2π$ twist. Notably, in $2d$, a Type II Hamiltonian with van der Waals interaction is subject to the constraint of the theorem. |
| title | Lieb-Schultz-Mattis Theorem with Long-Range Interactions |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2405.14949 |