2026/03/11 by Zhao Zhang · 1 voice
Physics and Astronomy · #nlin.SI #cond-mat.stat-mech #hep-th #math-ph #quant-ph
arxiv published 2026/03/11 · arxiv updated 2026/06/10
One-dimensional integrable fermions can be classified into massless and massive regimes, and the R-operator for the latter can be constructed from that of the former. Here, I define integrable massless fermions by the simultaneous satisfaction of the Yang-Baxter equation (YBE) and Shastry's decorated YBE (DYBE) by the R-matrix. This notion is strictly more general than Maassarani's `free-fermion algebra', yet more restrictive than the notion of free fermions in exactly solvable quantum models or in integrable two-dimensional classical vertex models dual to quantum spin chains. Within this framework, there emerge two archetypal mechanisms for opening a spectral gap and generating massive fermions: (i) breaking time-reversal symmetry by coupling to external field, and (ii) introducing time-reversal symmetric interactions. These paradigms are realized, respectively, in the XY chain in a longitudinal field and in the Hubbard model, both of which possess non-relativistic, bivariate R-matrices. Integrability conditions on local Hamiltonians for both massless and massive fermions are identified, and schematic procedures for uniquely determining their R-matrices are proposed.