The phases of the disordered Bose-Hubbard model with attractive interactions

TL;DR

This paper explores the ground state phases of a disordered one-dimensional attractive Bose-Hubbard model, revealing unique localization and entanglement behaviors distinct from the repulsive case, with implications for quantum simulation.

Contribution

It provides a detailed phase diagram of the disordered attractive Bose-Hubbard model using perturbation theory and exact diagonalization, highlighting novel localization and entanglement phenomena.

Findings

Bosons localize at a single site under strong disorder.

Weak disorder leads to superfluid or W states depending on hopping.

W state's robustness decreases with more bosons.

Abstract

We study the quantum ground state phases of the one-dimensional disordered Bose--Hubbard model with attractive interactions, realized by a chain of superconducting transmon qubits or cold atoms. We map the phase diagram using perturbation theory and exact diagonalization. Compared to the repulsive Bose--Hubbard model, the quantum ground state behavior is dramatically different. At strong disorder of the on-site energies, all the bosons localize into the vicinity of a single site, contrary to the Bose glass behavior of the repulsive model. At weak disorder, depending on hopping, the ground state is either superfluid or a W state, which is a multi-site and multi-particle entangled superposition of states where all the bosons occupy a single site. We show that the robustness of the W phase against disorder diminishes as the total number of bosons increases.