Hidden Grassmann Structure in the XXZ Model IV: CFT limit

TL;DR

This paper explores the Grassmann structure of the critical XXZ spin chain as it approaches conformal field theory, proposing a new fermionic description of Virasoro modules and relating it to traditional methods.

Contribution

It introduces a novel fermionic framework for Virasoro modules in the CFT limit of the XXZ model, connecting integrals of motion with algebraic structures.

Findings

New fermionic description of Virasoro modules

Exact relation to traditional Virasoro modules up to level 6

Enhanced understanding of the XXZ model's CFT limit

Abstract

The Grassmann structure of the critical XXZ spin chain is studied in the limit to conformal field theory. A new description of Virasoro Verma modules is proposed in terms of Zamolodchikov's integrals of motion and two families of fermionic creation operators. The exact relation to the usual Virasoro description is found up to level 6.