Quantum phases of supersymmetric lattice models

TL;DR

This paper reviews recent findings on supersymmetric lattice models for spin-less fermions, highlighting critical behavior in 1D and superfrustration with extensive ground state entropy in 2D, along with a potential new 'supertopological' phase.

Contribution

It provides a comprehensive review of supersymmetric lattice models, including analytical insights into ground state structures and the identification of novel quantum phases.

Findings

1D models exhibit superconformal critical behavior.

2D models show superfrustration with extensive ground state entropy.

Evidence of a new 'supertopological' phase in certain 2D lattices.

Abstract

We review recent results on lattice models for spin-less fermions with strong repulsive interactions. A judicious tuning of kinetic and interaction terms leads to a model possessing supersymmetry. In the 1D case, this model displays critical behavior described by superconformal field theory. On 2D lattices we generically find superfrustration, characterized by an extensive ground state entropy. For certain 2D lattices analytical results on the ground state structure reveal yet another quantum phase, which we tentatively call 'supertopological'.