Frustration-free free fermions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910277839093760 |
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| author | Ono, Seishiro Masaoka, Rintaro Watanabe, Haruki Po, Hoi Chun |
| author_facet | Ono, Seishiro Masaoka, Rintaro Watanabe, Haruki Po, Hoi Chun |
| contents | We develop a general theory of frustration-free free-fermion systems and derive the necessary and sufficient conditions for such Hamiltonians. Assuming locality and translation invariance, we find that any band touching between the valence and the conduction bands is always quadratic or softer, which rules out the possibility of describing Dirac and Weyl semimetals using frustration-free local Hamiltonians. We further construct a frustration-free free-fermion model on the honeycomb lattice and show that its density fluctuations acquire an anomalous gap originating from the diverging quantum metric associated with the quadratic band-touching points. Nevertheless, an $O(1/L^2)$ finite-size scaling of the charge-neutral excitation gap can be verified even in the presence of interactions, consistent with the more general results we derive in an accompanying work [arXiv:2503.12879]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14312 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frustration-free free fermions Ono, Seishiro Masaoka, Rintaro Watanabe, Haruki Po, Hoi Chun Strongly Correlated Electrons Other Condensed Matter Statistical Mechanics Quantum Physics We develop a general theory of frustration-free free-fermion systems and derive the necessary and sufficient conditions for such Hamiltonians. Assuming locality and translation invariance, we find that any band touching between the valence and the conduction bands is always quadratic or softer, which rules out the possibility of describing Dirac and Weyl semimetals using frustration-free local Hamiltonians. We further construct a frustration-free free-fermion model on the honeycomb lattice and show that its density fluctuations acquire an anomalous gap originating from the diverging quantum metric associated with the quadratic band-touching points. Nevertheless, an $O(1/L^2)$ finite-size scaling of the charge-neutral excitation gap can be verified even in the presence of interactions, consistent with the more general results we derive in an accompanying work [arXiv:2503.12879]. |
| title | Frustration-free free fermions |
| topic | Strongly Correlated Electrons Other Condensed Matter Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2503.14312 |