Boundary emptiness formation probabilities in the six-vertex model at ∆ = −1/2
(2020) Journal of Physics A: Mathematical and Theoretical —
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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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Morin Duchesne, A., Walmsley Hagendorf, C., & Cantini, L. (2020). Boundary emptiness formation probabilities in the six-vertex model at ∆ = −1/2. Journal of Physics A: Mathematical and Theoretical. https://hdl.handle.net/2078.5/122337