Abstract
We investigate the Rényi entanglement entropies for the one-dimensional massless free boson compactified on a circle, which describes the low energy sector of several interacting many-body 1d systems (Luttinger Liquid). We focus on systems on a finite segment with open boundary conditions and possible inhomogeneities in the couplings. We provide expressions for the Rényi entropies of integer indices in terms of Fredholm determinant-like expressions. Within the homogeneous case, we reduce the problem to the solution of linear integral equations and the computation of Riemann Theta functions. We mainly focus on a single interval in the middle of the system, but results for generic bipartitions are given as well.
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Bastianello, A. Rényi entanglement entropies for the compactified massless boson with open boundary conditions. J. High Energ. Phys. 2019, 141 (2019). https://doi.org/10.1007/JHEP10(2019)141
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DOI: https://doi.org/10.1007/JHEP10(2019)141