Continuum Limit of gl(M/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.

References in corpus (6)

• On the SU(2|1) WZW model and its statistical mechanics applications
• The GL(1|1)-symplectic fermion correspondence
• A lattice approach to the conformal $\OSp(2S+2|2S)$ supercoset sigma model. Part I: Algebraic structures in the spin chain. The Brauer algebra
• Finite size properties of staggered $U_q[sl(2|1)]$ superspin chains
• A lattice approach to the conformal $\OSp(2S+2|2S)$ supercoset sigma model. Part II: The boundary spectrum
• Exact solution and finite size properties of the $U_q[osp(2|2m)]$ vertex model

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