Continuum limit of gl(M$\vert$N) spin chains

Abstract

We study the spectrum of an integrable antiferromagnetic Hamiltonian of the gl(M|N) spin chain of alternating fundamental and dual representations. After extensive numerical analysis, we identify the vacuum and low lying excitations and with this knowledge perform the continuum limit, while keeping a finite gap. All gl(n+N|N) spin chains with n,N>0 are shown to possess in the continuum limit 2n-2 multiplets of massive particles which scatter with gl(n) Gross-Neveu like S-matrices, namely their eigenvalues do not depend on N. We argue that the continuum theory is the gl(M|N) Gross-Neveu model. We then look for remaining particles in the gl(2m|1) chains. The results suggest there is a continuum of such particles, which in order to be fully understood require finite volume calculations