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

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 $U_q(\widehat{s{l}_2})$.

27 pages, 3 figures

References in corpus (4)

• The eight-vertex model and Painleve VI
• Sum rules for the ground states of the O(1) loop model on a cylinder and the XXZ spin chain
• Polynomial solutions of qKZ equation and ground state of XXZ spin chain at Delta = -1/2
• Combinatorial point for higher spin loop models

Cited by in corpus (13)

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• Formation probabilities in quantum critical chains and Casimir effect
• Emptiness formation probability and Painlevé V equation in the XY spin chain
• Finite size corrections to scaling of the formation probabilities and the Casimir effect in the conformal field theories
• The nineteen-vertex model and alternating sign matrices
• Boundary emptiness formation probabilities in the six-vertex model at $\Delta =-\frac{1}{2}$
• Symmetry classes of alternating sign matrices in the nineteen-vertex model
• Sum rules for the supersymmetric eight-vertex model
• On the logarithmic bipartite fidelity of the open XXZ spin chain at $\Delta =-1/2$
• On Baxter's Q operator of the higher spin XXZ chain at the Razumov-Stroganov point
• The open XXZ chain at $\Delta =-1/2$ and the boundary quantum Knizhnik-Zamolodchikov equations