A q-Virasoro Algebra at roots of unity, Free Fermions and Temperley Lieb Hamiltonians

TL;DR

This paper introduces a new q-deformation of the Virasoro algebra using free fermions, which can be exactly realized on a lattice at roots of unity, and explores its relation to Temperley-Lieb Hamiltonians.

Contribution

It presents a novel q-deformation of the Virasoro algebra at roots of unity and establishes its exact lattice realization and connection to Temperley-Lieb Hamiltonians.

Findings

Exact lattice realization of the deformed Virasoro algebra at roots of unity

Relation between the algebra and Temperley-Lieb Hamiltonians

New insights into lattice models and algebraic structures

Abstract

In this work we introduce a novel q-deformation of the Virasoro algebra expressed in terms of free fermions, we then realize that this algebra, when the deformation parameter is a root of unity can be realized exactly on the lattice. We then study the relations existing between this lattice deformed Virasoro algebra at roots of unity and the tower of commuting Temperley-Lieb hamiltonians introduced in a previous work.