2026/07/22 by Hao Cheng, Hang Su, Yuan Yao
#cond-mat.str-el #cond-mat.stat-mech #hep-th #math-ph #math.MP
We propose a general necessary condition for a spinful fermion chain with SU(2) spin-rotation symmetry to be gapped. Specifically, we prove that the expectation value of a properly defined fermionic twisting operator asymptotically approaches unity in any gapped phase with finite ground-state degeneracy, with finite-size corrections bounded by \mathscrO(1/L). Consequently, a non-unity value in the thermodynamic limit provides a sufficient criterion for identifying gapless fermion chains. We confirm this criterion using the s-wave Bardeen-Cooper-Schrieffer (BCS) Hamiltonian and determinant quantum Monte Carlo (DQMC) simulations of interacting Hubbard models. We further extend the twisting-operator approach to SU(N)-symmetric fermionic systems, where the gapped ground-state sector must be SU(N)-singlet and ⟨ UM⟩=1+\mathscrO(1/L) by a fermionic twisting operator U with a suitably chosen integer M.