Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-10-26
J. Phys. A: Math. Theor. 45 (2012) 105206
Physics
Condensed Matter
Statistical Mechanics
LaTex, 1+23 pages, 5 figures, typos corrected, analytic derivation of the integer Renyi entaglement entropies added in section
Scientific paper
10.1088/1751-8113/45/10/105206
We consider a fermion gas on a star graph modeling a quantum wire junction and derive the entanglement entropy of one edge with respect to the rest of the junction. The gas is free in the bulk of the graph, the interaction being localized in its vertex and described by a non-trivial scattering matrix. We discuss all point-like interactions, which lead to unitary time evolution of the system. We show that for a finite number of particles N, the Renyi entanglement entropies of one edge grow as ln N with a calculable prefactor, which depends not only on the central charge, but also on the total transmission probability from the considered edge to the rest of the graph. This result is extended to the case with an harmonic potential in the bulk.
Calabrese Pasquale
Mintchev Mihail
Vicari Ettore
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