A staggered fermion chain with supersymmetry on open intervals

TL;DR

This paper studies a supersymmetric fermion chain with staggered couplings on open boundaries, revealing connections to Painlevé VI solutions and scale-free properties enabling exact analysis of ground states.

Contribution

It introduces a novel staggered fermion chain model with supersymmetry, exploring ground state properties and uncovering links to nonlinear recursion relations and scale-free phenomena.

Findings

Ground states connected to Painlevé VI solutions

Scale-free properties in local occupation probabilities

Exact resummation possible in infinite system limit

Abstract

A strongly-interacting fermion chain with supersymmetry on the lattice and open boundary conditions is analysed. The local coupling constants of the model are staggered, and the properties of the ground states as a function of the staggering parameter are examined. In particular, a connection between certain ground-state components and solutions of non-linear recursion relations associated with the Painlev\'e VI equation is conjectured. Moreover, various local occupation probabilities in the ground state have the so-called scale-free property, and allow for an exact resummation in the limit of infinite system size.