### 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.

Original language | English |
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Article number | 023631 |

Number of pages | 12 |

Journal | Physical Review A: Atomic, Molecular, and Optical Physics |

Volume | 86 |

Issue number | 2 |

Early online date | 24 Aug 2012 |

DOIs | |

Publication status | Published - Aug 2012 |

### Keywords

- cond-mat.quant-gas
- quant-ph

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## Cite this

Pino, M., Prior, J., Somoza, A. M., Jaksch, D., & 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]. https://doi.org/10.1103/PhysRevA.86.023631