Hermann Boos

Hidden Grassmann Structure in the XXZ Model II: Creation Operators

In this article we unveil a new structure in the space of operators of the XXZ chain. For each α we consider the space

A RECURSION FORMULA FOR THE CORRELATION FUNCTIONS OF AN INHOMOGENEOUS XXX MODEL

{\mathcal W_\alpha}

Computation of Static Heisenberg-Chain Correlators: Control over Length and Temperature Dependence

of all quasi-local operators, which are products of the disorder field

Universal integrability objects

{q^{\alpha \sum_{j=-\infty}^0\sigma ^3_j}}

Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States

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 b(ζ), c(ζ) which mutually anti-commute and kill the “primary field”. Here we construct the creation counterpart b*(ζ), c*(ζ) and prove the canonical anti-commutation relations with the annihilation operators. We conjecture that the creation operators mutually anti-commute, thereby upgrading the Grassmann structure to the fermionic structure. The bosonic operator t*(ζ) is the generating function of the adjoint action by local integrals of motion, and commutes entirely with the fermionic creation and annihilation operators. Operators b*(ζ), c*(ζ), t*(ζ) create quasi-local operators starting from the primary field. We show that the ground state averages of quasi-local operators created in this way are given by determinants.

Oscillator versus prefundamental representations

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.