Eigenvalue spectrum of interacting massive fermions in one dimension

Abstract

The excitation spectrum of massive fermions with self-interaction moving in one space dimension is calculated, using exact solutions for the spin-1/2 chain problem. This spectrum is shown to be the same as in the massive Thirring model, sine-Gordon equation, and Tomonaga-Luttinger with gap, with suitable relations between coupling constants. Solitons and bound solitons occur, corresponding to magnons and bound magnons in the spin chain. The soliton mass is calculated as a function of lattice spacing, and the ratio of binding energy to soliton mass is shown to be given correctly by the WKB approximation.