Mott lobes of the $S=1$ Bose-Hubbard model with three-body interactions

TL;DR

This study uses the density matrix renormalization group to analyze the phase diagram of the one-dimensional $S=1$ Bose-Hubbard model with three-body interactions, revealing effects on Mott lobes and phase transitions.

Contribution

It provides the first detailed phase diagram of the $S=1$ Bose-Hubbard model with three-body interactions, highlighting the impact on Mott lobes and transition types.

Findings

Mott lobes decrease with increasing spin-dependent strength

Absence of even-odd asymmetry in Mott lobes due to three-body interactions

First-order superfluid-Mott insulator transitions driven by density

Abstract

Using the density matrix renormalization group method, we studied the ground state of the one-dimensional $S=1$ Bose-Hubbard model with local three-body interactions, which can be a superfluid or a Mott insulator state. We drew the phase diagram of this model for both ferromagnetic and antiferromagnetic interaction. Regardless of the sign of the spin-dependent coupling, we obtained that the Mott lobes area decreases as the spin-dependent strength increases, which means that the even-odd asymmetry of the two-body antiferromagnetic chain is absent for local three-body interactions. For antiferromagnetic coupling, we found that the density drives first-order superfluid-Mott insulator transitions for even and odd lobes. Ferromagnetic Mott insulator and superfluid states were obtained with a ferromagnetic coupling, and a tendency to a "long-range" order was observed.