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Abstract: We study the effects of a power-law trapping potential on the scalingbehaviour of the entanglement at the quantum critical point of one-dimensional1D lattice particle systems. We compute bipartite von Neumann and Renyientropies in the presence of the trap, and analyze their scaling behaviour withincreasing the trap size. As a theoretical laboratory, we consider the quantumXY chain in an external transverse field acting as a trap for the spinlessfermions of its quadratic Hamiltonian representation. We then investigateconfined particle systems described by the 1D Bose-Hubbard model in thesuperfluid phase around the center of the trap. In both cases conformal fieldtheory predicts logarithmically divergent bipartite entanglement entropies forthe homogeneous systems without trap. The presence of the trapping potentialbreaks conformal invariance, affecting the critical behaviour of thehomogeneous system. Our results show that the bipartite entanglement entropiesdiverge logarithmically with increasing the trap size, and present notablescaling behaviours in the trap-size scaling limit.



Autor: Massimo Campostrini, Ettore Vicari

Fuente: https://arxiv.org/







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