# Quantum phase transitions in the dimerized extended Bose-Hubbard model

## TL;DR

This study uses density-matrix renormalization group techniques to map the phase diagram of a one-dimensional dimerized extended Bose-Hubbard model, revealing various insulating phases, phase transitions, and critical behaviors including a topological Haldane insulator.

## Contribution

It provides the first detailed numerical analysis of the phase diagram, identifying the emergence and disappearance of the Haldane insulator and characterizing the universality classes of phase transitions.

## Key findings

- Discovery of a symmetry-protected topological Haldane insulator phase.
- Identification of Gaussian and Ising universality classes for phase boundaries.
- Observation of a tricritical point and a first-order transition at high Coulomb interactions.

## Abstract

We present an unbiased numerical density-matrix renormalization group study of the one-dimensional Bose-Hubbard model supplemented by nearest-neighbor Coulomb interaction and bond dimerization. It places the emphasis on the determination of the ground-state phase diagram and shows that, besides dimerized Mott and density-wave insulating phases, an intermediate symmetry-protected topological Haldane insulator emerges at weak Coulomb interactions for filling factor one, which disappears, however, when the dimerization becomes too large. Analyzing the critical behavior of the model, we prove that the phase boundaries of the Haldane phase to Mott insulator and density-wave states belong to the Gaussian and Ising universality classes with central charges $c=1$ and $c=1/2$, respectively, and merge in a tricritical point. Interestingly we can demonstrate a direct Ising quantum phase transition between the dimerized Mott and density-wave phases above the tricritical point. The corresponding transition line terminates at a critical end point that belongs to the universality class of the dilute Ising model with $c=7/10$. At even stronger Coulomb interactions the transition becomes first order.