Charge frustration and quantum criticality for strongly correlated fermions

TL;DR

This paper investigates a strongly correlated electron model on a square lattice, revealing charge frustration, quantum criticality, and supersymmetry, with implications for ground state degeneracy and edge modes.

Contribution

It establishes a rigorous link between quantum ground states and lattice tilings, and analyzes boundary condition effects on the system's gapless edge modes.

Findings

Ground state degeneracy grows exponentially with system size.

Presence of gapless edge modes under open boundary conditions.

Model exhibits charge frustration and quantum critical behavior.

Abstract

We study a model of strongly correlated electrons on the square lattice which exhibits charge frustration and quantum critical behavior. The potential is tuned to make the interactions supersymmetric. We establish a rigorous mathematical result which relates quantum ground states to certain tiling configurations on the square lattice. For periodic boundary conditions this relation implies that the number of ground states grows exponentially with the linear dimensions of the system. We present substantial analytic and numerical evidence that for open boundary conditions the system has gapless edge modes.