Capturing the re-entrant behaviour of one-dimensional Bose-Hubbard model

M. Pino, J. Prior, S. R. Clark

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The Bose Hubbard model (BHM) is an archetypal quantum lattice system exhibiting a quantum phase transition between its superfluid (SF) and Mott-insulator (MI) phase. Unlike in higher dimensions the phase diagram of the BHM in one dimension possesses regions in which increasing the hopping amplitude can result in a transition from MI to SF and then back to a MI. This type of re-entrance is well known in classical systems like liquid crystals yet its origin in quantum systems is still not well understood. Moreover, this unusual re-entrant character of the BHM is not easily captured in approximate analytical or numerical calculations. Here we study in detail the predictions of three different and widely used approximations; a multi-site mean-field decoupling, a finite-sized cluster calculation, and a real-space renormalization group (RG) approach. It is found that mean-field calculations do not reproduce re-entrance while finite-sized clusters display a precursor to re-entrance. Here we show for the first time that RG does capture the re-entrant feature and constitutes one of the simplest approximation able to do so. The differing abilities of these approaches reveals the importance of describing short-ranged correlations relevant to the kinetic energy of a MI in a particle-number symmetric way.
Original languageEnglish
Pages (from-to)51-58
JournalPhysica Status Solidi (C)
Issue number1
Early online date10 Dec 2012
Publication statusPublished - Jan 2013

Bibliographical note

To appear in Physica Status Solidi (b). 8 pages, 4 figures


  • cond-mat.quant-gas
  • quant-ph


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