Frustration-free free fermions and beyond

• URL: http://arxiv.org/abs/2503.12879v1
• Date: Mon, 17 Mar 2025 07:18:15 GMT
• Title: Frustration-free free fermions and beyond
• Authors: Rintaro Masaoka, Seishiro Ono, Hoi Chun Po, Haruki Watanabe,
• Abstract summary: Frustration-free Hamiltonians provide pivotal models for understanding quantum many-body systems.<n>We establish a general framework for frustration-free fermionic systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $\eta$-pairing states.

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