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Re-entrance and entanglement in the one-dimensional Bose-Hubbard model


Reference:

Pino, M., Prior, J., Somoza, A. M., Jaksch, D. and Clark, S. R., 2012. Re-entrance and entanglement in the one-dimensional Bose-Hubbard model. Physical Review A: Atomic, Molecular, and Optical Physics, 86 (2), 023631.

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    Official URL:

    http://dx.doi.org/10.1103/PhysRevA.86.023631

    Abstract

    Re-entrance is a novel feature where the phase boundaries of a system exhibit a succession of transitions between two phases A and B, like A-B-A-B, when just one parameter is varied monotonically. This type of re-entrance is displayed by the 1D Bose Hubbard model between its Mott insulator (MI) and superfluid phase as the hopping amplitude is increased from zero. Here we analyse this counter-intuitive phenomenon directly in the thermodynamic limit by utilizing the infinite time-evolving block decimation algorithm to variationally minimize an infinite matrix product state (MPS) parameterized by a matrix size chi. Exploiting the direct restriction on the half-chain entanglement imposed by fixing chi, we determined that re-entrance in the MI lobes only emerges in this approximate when chi >= 8. This entanglement threshold is found to be coincident with the ability an infinite MPS to be simultaneously particle-number symmetric and capture the kinetic energy carried by particle-hole excitations above the MI. Focussing on the tip of the MI lobe we then applied, for the first time, a general finite-entanglement scaling analysis of the infinite order Kosterlitz-Thouless critical point located there. By analysing chi's up to a very moderate chi = 70 we obtained an estimate of the KT transition as t_KT = 0.30 +/- 0.01, demonstrating the how a finite-entanglement approach can provide not only qualitative insight but also quantitatively accurate predictions.

    Details

    Item Type Articles
    CreatorsPino, M., Prior, J., Somoza, A. M., Jaksch, D. and Clark, S. R.
    DOI10.1103/PhysRevA.86.023631
    Uncontrolled Keywordscond-mat.quant-gas,quant-ph
    DepartmentsFaculty of Science > Physics
    RefereedYes
    StatusPublished
    ID Code47336
    Additional Information12 pages, 8 figures

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