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Frustration-free free fermions

Seishiro Ono1,2,3, Rintaro Masaoka4, Haruki Watanabe2,4,5,6,*, and Hoi Chun Po2,6,†

  • *Contact author: hwatanabe@ust.hk
  • †Contact author: hcpo@ust.hk
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Phys. Rev. Research 8, 023171 – Published 15 May, 2026

DOI: https://doi.org/10.1103/9mt9-9fjr

Abstract

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/L2) 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 [Masaoka et al., Phys. Rev. B 113, 195120 (2026)].

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Frustration-free fermionic systems: Finite-size scaling and band topology

Rintaro Masaoka, Seishiro Ono, Hoi Chun Po, and Haruki Watanabe
Phys. Rev. B 113, 195120 (2026)

Article Text

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Phys. Rev. Research 8, 023171– Published 15 May, 2026
  • Received 7 April 2025
  • Revised 6 January 2026
  • Accepted 9 April 2026
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