Quadratic dispersion relations in gapless frustration-free systems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913606744932352 |
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| author | Masaoka, Rintaro Soejima, Tomohiro Watanabe, Haruki |
| author_facet | Masaoka, Rintaro Soejima, Tomohiro Watanabe, Haruki |
| contents | Recent case-by-case studies revealed that the dispersion of low energy excitations in gapless frustration-free Hamiltonians is often quadratic or softer. In this work, we argue that this is actually a general property of such systems. By combining a previous study by Bravyi and Gosset and the min-max principle, we prove this hypothesis for models with local Hilbert spaces of dimension two that contains only nearest-neighbor interactions on cubic lattice. This may be understood as a no-go theorem realizing gapless phases with linearly dispersive excitations in frustration-free Hamiltonians. We also provide examples of frustration-free Hamiltonians in which the plane-wave state of a single spin flip does not constitute low energy excitations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_06414 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quadratic dispersion relations in gapless frustration-free systems Masaoka, Rintaro Soejima, Tomohiro Watanabe, Haruki Strongly Correlated Electrons Other Condensed Matter Statistical Mechanics Quantum Physics Recent case-by-case studies revealed that the dispersion of low energy excitations in gapless frustration-free Hamiltonians is often quadratic or softer. In this work, we argue that this is actually a general property of such systems. By combining a previous study by Bravyi and Gosset and the min-max principle, we prove this hypothesis for models with local Hilbert spaces of dimension two that contains only nearest-neighbor interactions on cubic lattice. This may be understood as a no-go theorem realizing gapless phases with linearly dispersive excitations in frustration-free Hamiltonians. We also provide examples of frustration-free Hamiltonians in which the plane-wave state of a single spin flip does not constitute low energy excitations. |
| title | Quadratic dispersion relations in gapless frustration-free systems |
| topic | Strongly Correlated Electrons Other Condensed Matter Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2406.06414 |