# Bosonic Haldane insulator in the presence of local disorder: A quantum Monte Carlo study

## TL;DR

This study uses quantum Monte Carlo simulations to investigate the robustness and phase transitions of the bosonic Haldane phase under local disorder in an extended Bose-Hubbard model, revealing its stability and complex phase behavior.

## Contribution

It provides the first detailed phase diagram showing the stability of the bosonic Haldane phase with disorder and uncovers a direct transition to superfluidity.

## Key findings

- Haldane phase is robust against weak disorder.
- Non-local string order exhibits reentrant behavior.
- Direct transition from Haldane to superfluid phase is observed.

## Abstract

The Haldane phase (HP) is a paradigmatic example of symmetry protected topological phase. We explore how the bosonic HP behaves in the presence of local disorder, employing quantum Monte Carlo simulations of an extended Bose-Hubbard model subject to uncorrelated, quenched disorders. We find that the HP is robust against a weak disorder and the non-local string order of HP exhibits a reentrant behavior. Besides, a direct transition between the HP and superfluid phase is uncovered. A significant part of the ground-state phase diagram is established for the model, unveiling the location of HP surrounded by Bose glass, charge density wave and superfluid phases. We also mention a possible experimental scheme with optical lattice emulator to realize the present findings.