Hidden Grassmann Structure in the XXZ Model II: Creation Operators

TL;DR

This paper reveals a new algebraic structure in the XXZ spin chain involving creation and annihilation operators that satisfy canonical anti-commutation relations, leading to determinant formulas for ground state averages.

Contribution

It introduces creation operators that complement previously known annihilation operators, establishing a canonical anti-commutation algebra in the XXZ model.

Findings

Creation operators are constructed and shown to satisfy anti-commutation relations.

Ground state averages of created operators are expressed as determinants.

The structure parallels conformal field theory concepts.

Abstract

In this article we unveil a new structure in the space of operators of the XXZ chain. We consider the space of all quasi-local operators, which are products of the disorder field with arbitrary local operators. In analogy with CFT the disorder operator itself is considered as primary field. In our previous paper, we have introduced the annhilation operators which mutually anti-commute and kill the primary field. Here we construct the creation counterpart and prove the canonical anti-commutation relations with the annihilation operators. We show that the ground state averages of quasi-local operators created by the creation operators from the primary field are given by determinants.