New family of models for incompressible quantum liquids in $d\geq 2$

TL;DR

This paper introduces a new class of SU(N) spin Hamiltonians in higher dimensions, generalizing previous models to describe fractionalized excitations in quantum liquids.

Contribution

It generalizes Haldane's construction to SU(N) models in dimensions d≥2, proposing a novel class of models with potential fractional excitations.

Findings

New SU(N) spin Hamiltonians for d≥2

Models describe center-of-mass conserving pair hopping fermions

Conjecture of fractional fermion number excitations

Abstract

Through Haldane's construction, the fractional quantum Hall states on a two-sphere was shown to be the ground states of {\it one-dimensional} SU(2) spin Hamiltonians. In this Letter we generalize this construction to obtain a new class of SU(N) spin Hamiltonians. These Hamiltonians describes center-of-mass-position conserving pair hopping fermions in space dimension $d\ge 2$. We conjecture that the excitations of these models posses fractional fermion number.