Phases, transitions, and patterns in the one-dimensional Extended Bose-Hubbard model

TL;DR

This paper extensively maps the phase diagram of the one-dimensional extended Bose-Hubbard model, revealing multiple phases and complex transitions, including potentially exotic behavior in the superfluid-Haldane insulator transition.

Contribution

It provides a detailed analysis of the phase diagram and critical properties of the 1D extended Bose-Hubbard model using DMRG, identifying various phases and their universality classes.

Findings

Identification of SF, MI, DW, and HI phases depending on parameters.

Critical exponents match known universality classes for certain transitions.

Potentially exotic nature of the SF-HI transition.

Abstract

We carry out an extensive study of the phase diagram of the extended Bose Hubbard model, with a mean filling of one boson per site, in one dimension by using the density matrix renormalization group and show that it can have Superfluid (SF), Mott-insulator (MI), density-wave (DW) and Haldane-insulator (HI) phases depending on the precise value of filling and how edge states are handled. We show that the critical exponents and central charge for the HI-DW, MI-HI and SF-MI transitions are consistent with those for models in the two-dimensional Ising, Gaussian, and Berezinskii-Kosterlitz-Thouless (BKT) universality classes, respectively; and we suggest that the SF-HI transition may be more exotic than a simple BKT transition.