Ground states of Nicolai and $\mathbb{Z}_2$ Nicolai models

TL;DR

This paper derives explicit recursive formulas for the ground state generating functions of one-dimensional Nicolai and $ Z_2$ Nicolai models, confirming numerical predictions and advancing understanding of supersymmetric lattice models.

Contribution

It provides the first explicit recursive relations for the ground states of these supersymmetric lattice models, validating previous numerical predictions.

Findings

Derived explicit recursion relations for ground state generating functions.

Confirmed numerical predictions for the $ Z_2$ Nicolai model.

Enhanced understanding of supersymmetry in lattice models.

Abstract

We derive explicit recursions for the ground state generating functions of the one-dimensional Nicolai model and $\mathbb{Z}_2$ Nicolai model. Both are examples of lattice models with $\mathcal{N}=2$ supersymmetry. The relations that we obtain for the $\mathbb{Z}_2$ model were numerically predicted by Sannomiya, Katsura, and Nakayama.