Extensive ground state entropy in supersymmetric lattice models

TL;DR

This paper calculates the Witten index for a supersymmetric lattice model, showing it grows exponentially with system size, indicating extensive ground state entropy, which suggests highly degenerate ground states in such models.

Contribution

It provides the first numerical evidence that the ground state entropy in supersymmetric lattice models is extensive, using transfer matrix methods to compute the Witten index.

Findings

Witten index grows exponentially with lattice size

Ground state entropy is extensive in the model

Numerical methods confirm high ground state degeneracy

Abstract

We present the result of calculations of the Witten index for a supersymmetric lattice model on lattices of various type and size. Because the model remains supersymmetric at finite lattice size, the Witten index can be calculated using row-to-row transfer matrices and the calculations are similar to calculations of the partition function at negative activity -1. The Witten index provides a lower bound on the number of ground states. We find strong numerical evidence that the Witten index grows exponentially with the number of sites of the lattice, implying that the model has extensive entropy in the ground state.