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arXiv · 1911.08972

Boundary emptiness formation probabilities in the six-vertex model at $\Delta = -\frac12$

Alexi Morin-Duchesne·Christian Hagendorf·Luigi Cantini
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Abstract

We define a new family of overlaps $C_{N,m}$ for the XXZ Hamiltonian on a periodic chain of length $N$. These are equal to the linear sums of the groundstate components, in the canonical basis, wherein $m$ consecutive spins are fixed to the state ${\uparrow}$. We define the boundary emptiness formation probabilities as the ratios $C_{N,m}/C_{N,0}$ of these overlaps. In the associated six-vertex model, they correspond to correlation functions on a semi-infinite cylinder of perimeter $N$. At the combinatorial point $\Delta = -\frac12$, we obtain closed-form expressions in terms of simple products of ratios of integers.

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Alexi Morin-Duchesne, Christian Hagendorf, Luigi Cantini. 2019-11-20. Boundary emptiness formation probabilities in the six-vertex model at $\Delta = -\frac12$. https://doi.org/10.1088/1751-8121%2Fab8507

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