Continuum Limit of gl(M/N) Spin Chains

TL;DR

This paper investigates the continuum limit of gl(M|N) spin chains, revealing a connection to the gl(M|N) Gross-Neveu model and identifying massive particle multiplets with specific scattering properties.

Contribution

It provides the first detailed analysis of the continuum limit of gl(M|N) spin chains, establishing their relation to the gl(M|N) Gross-Neveu model and characterizing their particle spectrum.

Findings

gl(n+N|N) chains have 2n-2 multiplets of massive particles

These particles scatter with gl(n) Gross-Neveu like S-matrices

Continuum limit suggests a connection to the gl(M|N) Gross-Neveu model

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.