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

TL;DR

This paper investigates the quantum phase transition of spin-2 cold bosons in an optical lattice, revealing how the transition depends on interaction parameters and Zeeman levels, with phase diagrams illustrating the conditions for Mott insulator to superfluid transition.

Contribution

The study introduces a Bose-Hubbard model for spin-2 bosons, calculates phase diagrams considering perturbative hopping, and links phase boundaries to Zeeman level populations, providing new insights into spin-dependent quantum phase transitions.

Findings

Phase transition from Mott insulator to superfluid occurs at a critical ratio of interaction to hopping.

Phase boundaries vary with Zeeman level components and their populations.

Different Zeeman levels exhibit distinct phase boundary behaviors.

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.