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Progress of Theoretical Physics Supplement

From Multiple Integrals to Fredholm Determinants(Interaction and Nanostructural Effects in Low-Dimensional Systems)

Alexander Seel, Frank Göhmann, Andreas Klümper

Published Feb 5, 2009• 0 citations
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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.