On the ground states of the $M_{\ell }$ models

Abstract

We study the $M_{\ell }$ models for lattice fermions with supersymmetry introduced by Fendley, Nienhuis and Schoutens on one-dimensional chains. We determine the number of ground states as a function of the chain length as well as various boundary conditions by solving the corresponding cohomology problem. As an intermediate result we obtain the Cut (and Paste) cohomology isomorphism, which maps the cohomology problem of chains, whose lengths differ by $\ell +2$ sites, onto each other.

28 pages, 5 figures, 2 appendices

References in corpus (3)

• Charge frustration and quantum criticality for strongly correlated fermions
• Extensive ground state entropy in supersymmetric lattice models
• Ground-state properties of a supersymmetric fermion chain

Cited by in corpus (3)

• M${}_k$ models: the field theory connection
• Defects and degeneracies in supersymmetry protected phases
• Spinon bases in supersymmetric CFTs