Quantum Phase Transition of Spin-2 Cold Bosons in an Optical Lattice

Abstract

The Bose-Hubbard Hamiltonian of spin-2 cold bosons with repulsive interaction in an optical lattice is proposed. After neglecting the hopping term, the site-independent Hamiltonian and its energy eigenvalues and eigenstates are obtained. We consider the hopping term as a perturbation to do the calculations in second order and draw the phase diagrams for different cases. The phase diagrams show that there is a phase transition from Mott insulator with integer number bosons to superfluid when the ratio $c_0/t$ ($c_0$ is the spin-independent on-site interaction and $t$ the hopping matrix element between adjacent lattice sites) is decreased to a critical value and that there is different phase boundary between superfluid and Mott insulator phase for different Zeeman level component in some ground states. We find that the position of phase boundary for different Zeeman level component is related to its average population in the Mott ground state.

arXiv comment16 pages, 6 figures

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• Superfluid-Mott Insulator Transition of Spin-2 Cold Bosons in an Optical Lattice in a Magnetic Field
• Mott phases and superfluid-insulator transition of dipolar spin-three bosons in an optical lattice: implications for Cr atoms
• Singlet Mott State Simulating the Bosonic Laughlin Wave Function
• Hyperfine Spin-Two (F=2) Atoms in Three-Dimensional Optical Lattices: Phase Diagrams and Phase Transitions
• Spin-1 Bose Hubbard model with nearest neighbour extended interaction
• Rigorous Results for the Ground States of the Spin-2 Bose-Hubbard Model
• Quantum entanglement of spin-1 bosons with coupled ground states in optical lattices