Finite size emptiness formation probability of the XXZ spin chain at $\Delta=-1/2$

TL;DR

This paper calculates the finite size emptiness formation probability of the XXZ spin chain at a specific anisotropy, confirming previously conjectured formulas using quantum group symmetries and qKZ equations.

Contribution

It provides a rigorous proof of the conjectured formulas for the emptiness formation probability at =-1/2 for finite XXZ chains, leveraging qKZ equations and quantum group methods.

Findings

Confirmed conjectured formulas for finite XXZ chain at =-1/2

Connected ground state properties to qKZ equations and quantum groups

Validated the use of algebraic methods for finite-size quantum spin chains

Abstract

In this paper we compute the Emptiness Formation Probability of a (twisted-) periodic XXZ spin chain of finite length at $\Delta=-1/2$, thus proving the formulae conjectured by Razumov and Stroganov \cite{raz-strog1, raz-strog2}. The result is obtained by exploiting the fact that the ground state of the inhomogeneous XXZ spin chain at $\Delta=-1/2$ satisfies a set of qKZ equations associated to $\displaystyle{U_q(\hat{sl_2})}$.