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Journal of Physics Conference Series

Mott lobes evolution of the spin-1 Bose-Hubbard model

A. F. Hincapie-F, R Franco, Jereson Silva-Valencia

Published Feb 1, 2016• 1 citation
Publisher

Abstract

We study spin-1 bosons confined in a one-dimensional optical lattice, taking into consideration both ferromagnetic and antiferromagnetic interaction. Using the density matrix renormalization group, we determine the phase diagram for the two firsts lobes and report the evolution of the first and second Mott lobes with respect to the spin-exchange interaction parameter ( U 2 ). We determine that for the antiferromagnetic case, the first lobe is suppressed while the second grows as | U 2 | increases. For the ferromagnetic case, the first and second Mott lobes are suppressed by the spin-exchange interaction parameter. We propose an expresion to describe the evolution of the critical point with the increase in | U 2 | for both cases.

DOI
10.1088/1742-6596/687/1/012071

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We study spin-1 bosons confined in a one-dimensional optical lattice, taking into consideration both ferromagnetic and antiferromagnetic interaction. Using the density matrix renormalization group, we determine the phase diagram for the two firsts lobes and report the evolution of the first and second Mott lobes with respect to the spin-exchange interaction parameter ( U 2 ). We determine that for the antiferromagnetic case, the first lobe is suppressed while the second grows as | U 2 | increases. For the ferromagnetic case, the first and second Mott lobes are suppressed by the spin-exchange interaction parameter. We propose an expresion to describe the evolution of the critical point with the increase in | U 2 | for both cases.
Using the density-matrix renormalization-group method, we studied the ground state of the one-dimensional S=1S=1S=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.
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We study, using quantum Monte Carlo (QMC) simulations, the ground state properties of spin-1 bosons trapped in a square optical lattice. The phase diagram is characterized by the mobility of the particles (Mott insulating or superfluid phase) and by their magnetic properties. For ferromagnetic on-site interactions, the whole phase diagram is ferromagnetic and the Mott insulators-superfluid phase transitions are second order. For antiferromagnetic on-site interactions, spin nematic order is found in the odd Mott lobes and in the superfluid phase. Furthermore, the superfluid-insulator phase transition is first or second order depending on whether the density in the Mott is even or odd. Inside the even Mott lobes we observe a singlet-to-nematic transition for certain values of the interactions. This transition appears to be first order.
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