Reentrance is an unusual feature where the phase boundaries of a system exhibit a succession of transitions between two phases $A$ and $B$, such as $A$-$B$-$A$-$B$, when just one parameter is varied monotonically. This type of reentrance is displayed by the Bose-Hubbard model in one spatial dimension between its Mott insulator (MI) and superfluid phase as the hopping amplitude is increased from zero. Here we analyze this counterintuitive 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 reentrance in the MI lobes only emerges in this approximation when $\chi \ge 8$. This entanglement threshold is found to be coincident with the ability of an infinite MPS to be simultaneously particle-number symmetric and capture the kinetic energy carried by particle-hole excitations above the MI. Focusing on the tip of the MI lobe, we then applied a general finite-entanglement scaling analysis of the infinite-order Kosterlitz-Thouless (KT) critical point located there. By analyzing values of $\chi$ up to a very moderate $\chi =70$, we obtained an estimate of the KT transition as $t_{\mathrm{KT}}=0.30\pm 0.01$, demonstrating how a finite-entanglement approach can provide not only qualitative insight but also quantitatively accurate predictions.

• Received 1 June 2012

DOI:https://doi.org/10.1103/PhysRevA.86.023631