Frustration-free free fermions and beyond
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917193162162176 |
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| author | Masaoka, Rintaro Ono, Seishiro Po, Hoi Chun Watanabe, Haruki |
| author_facet | Masaoka, Rintaro Ono, Seishiro Po, Hoi Chun Watanabe, Haruki |
| contents | Frustration-free Hamiltonians provide pivotal models for understanding quantum many-body systems. In this paper, we establish a general framework for frustration-free fermionic systems. First, we derive a necessary and sufficient condition for a free fermion model to be frustration-free. In the case of translation-invariant, noninteracting systems, we show that any band touching between the valence and conduction bands is at least quadratic. Furthermore, by extending the Gosset-Huang inequality to fermionic systems, we demonstrate that even in interacting and non-translation-invariant cases, the finite-size gap of gapless excitations scales as $O((\log L)^2/L^2)$, provided the ground-state correlation function exhibits a power-law decay. Our results provide a foundation for studying frustration-free fermionic systems, including flat-band ferromagnetism and $η$-pairing states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12879 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frustration-free free fermions and beyond Masaoka, Rintaro Ono, Seishiro Po, Hoi Chun Watanabe, Haruki Strongly Correlated Electrons Other Condensed Matter Statistical Mechanics Quantum Physics Frustration-free Hamiltonians provide pivotal models for understanding quantum many-body systems. In this paper, we establish a general framework for frustration-free fermionic systems. First, we derive a necessary and sufficient condition for a free fermion model to be frustration-free. In the case of translation-invariant, noninteracting systems, we show that any band touching between the valence and conduction bands is at least quadratic. Furthermore, by extending the Gosset-Huang inequality to fermionic systems, we demonstrate that even in interacting and non-translation-invariant cases, the finite-size gap of gapless excitations scales as $O((\log L)^2/L^2)$, provided the ground-state correlation function exhibits a power-law decay. Our results provide a foundation for studying frustration-free fermionic systems, including flat-band ferromagnetism and $η$-pairing states. |
| title | Frustration-free free fermions and beyond |
| topic | Strongly Correlated Electrons Other Condensed Matter Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2503.12879 |