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

Abstract

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

Supersymmetry breaking and Nambu-Goldstone fermions in interacting Majorana chains

“…In the Nicolai model, the number of the ground states degeneracy grows exponentially with systems size. The classification of the ground states which are product states is discussed [31], and the number of the ground states of the Nicolai model is calculated using homology argument [32]. A part of the degeneracy can be understood from the first term in Eq.…”

“…Similar to the Nicolai model, this model shows superfrustration when g = 0, i.e., the number of the ground states degeneracy grows exponentially with system size N . The number of degenerated ground states is calculated using homology argument [32]. In this model, SUSY is spontaneously broken when g = 0 in finite systems and g > 4/π in the infinite volume limit.…”

Spontaneously broken supersymmetric fracton phases with fermionic subsystem symmetries

“…The Nicolai model is a supersymmetric lattice model whose Hamiltonian is constructed purely out of fermionic creation and annihilation operators. The ground states on the chain are exponentially degenerate with respect to the system size, and the structure of ground states has been extensively studied in the literature [29][30][31]. When the coupling constants are randomly generated, it may also be regarded as a supersymmetric analogue of the Sachdev-Ye-Kitaev model [34][35][36][37].…”

Topological quantum computation on supersymmetric spin chains

“…In general these models have an extensive ground state degeneracy, with exponentially growing numbers of states being the common trend more often than not [43][44][45][46][47][48]. Some of these supersymmetric spin chains have also shown to exhibit localization effects similar to many body localized systems [49,50] and these supercharges have been used to obtain solutions of the Yang-Baxter equation and its generalization [51].…”