Phases, transitions, and boundary conditions in a model of interacting bosons

TL;DR

This study explores the phase diagram of the extended Bose Hubbard model in one dimension, identifying multiple phases and analyzing the nature of phase transitions using advanced numerical methods.

Contribution

It provides a detailed analysis of phase transitions and boundary effects in the 1D extended Bose Hubbard model, highlighting the universality classes and potential exotic nature of some transitions.

Findings

Identification of SF, MI, DW, and HI phases in the model.

Critical exponents match known universality classes.

Boundary conditions significantly affect phase diagrams.

Abstract

We carry out an extensive study of the phase diagrams 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 contains Superfluid (SF), Mott-insulator (MI), density-wave (DW) and Haldane-insulator (HI) phases. We show that the critical exponents and central charges 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. We show explicitly that different boundary conditions lead to different phase diagrams.