Superfluid, Mott-Insulator, and Mass-Density-Wave Phases in the One-Dimensional Extended Bose-Hubbard Model

TL;DR

This study maps the phase diagram of the one-dimensional extended Bose-Hubbard model at density 1, revealing superfluid, Mott insulator, and mass density wave phases with detailed transition characterizations.

Contribution

It provides the first comprehensive phase diagram of the 1D extended Bose-Hubbard model using FSDMRG, identifying the nature of phase transitions and the bicritical point.

Findings

Reentrant superfluid-Mott insulator-superfluid transition at small interactions.

Continuous KT and Ising-like transitions between phases.

First-order transition between Mott insulator and mass density wave at large interactions.

Abstract

We use the finite-size density-matrix-renormalization-group (FSDMRG) method to obtain the phase diagram of the one-dimensional ($d = 1$) extended Bose-Hubbard model for density $\rho = 1$ in the $U-V$ plane, where $U$ and $V$ are, respectively, onsite and nearest-neighbor interactions. The phase diagram comprises three phases: Superfluid (SF), Mott Insulator (MI) and Mass Density Wave (MDW). For small values of $U$ and $V$, we get a reentrant SF-MI-SF phase transition. For intermediate values of interactions the SF phase is sandwiched between MI and MDW phases with continuous SF-MI and SF-MDW transitions. We show, by a detailed finite-size scaling analysis, that the MI-SF transition is of Kosterlitz-Thouless (KT) type whereas the MDW-SF transition has both KT and two-dimensional-Ising characters. For large values of $U$ and $V$ we get a direct, first-order, MI-MDW transition. The MI-SF, MDW-SF and MI-MDW phase boundaries join at a bicritical point at ($U, V) = (8.5 \pm 0.05, 4.75 \pm 0.05)$.