Exact ground states of a staggered supersymmetric model for lattice fermions

TL;DR

This paper analytically explores the ground states of a supersymmetric lattice fermion model with staggering, revealing crystalline, valence bond, and quantum liquid phases on various lattices, including a detailed 1D analysis.

Contribution

It provides exact ground state solutions for a staggered supersymmetric fermion model, highlighting phase transitions between crystalline, valence bond, and quantum liquid states.

Findings

Ground states include Wigner crystal and VBS in one limit.

Quantum liquids with massless kinks are found in another limit.

Detailed analysis of the 1D chain reveals a separation of order by a massless kink.

Abstract

We study a supersymmetric model for strongly interacting lattice fermions in the presence of a staggering parameter. The staggering is introduced as a tunable parameter in the manifestly supersymmetric Hamiltonian. We obtain analytic expressions for the ground states in the limit of small and large staggering for the model on the class of doubly decorated lattices. On this type of lattice there are two ground states, each with a different density. In one limit we find these ground states to be a simple Wigner crystal and a valence bond solid (VBS) state. In the other limit we find two types of quantum liquids. As a special case, we investigate the quantum liquid state on the one dimensional chain in detail. It is characterized by a massless kink that separates two types of order.