Magnetic phase diagram and quantum phase transitions in a two-species boson model

TL;DR

This paper explores the magnetic phase diagram and quantum phase transitions in a two-species boson model related to optical lattice systems, revealing complex magnetic phases and the effects of tuning interaction parameters.

Contribution

It introduces a reduction of a boson-fermion model to a spin-pseudospin model with spin 1 and pseudospin 1/2, uncovering novel magnetic phases and quantum transitions.

Findings

Ground state exhibits pseudospin domain structure.

Sign change in interaction parameter switches spin order within domains.

Quantum phase transitions are driven by tuning the spin-channel interaction.

Abstract

We analyze the possible types of ordering in a boson--fermion model. The Hamiltonian is inherently related to the Bose--Hubbard model for vector two-species bosons in optical lattices. We show that such model can be reduced to the Kugel--Khomskii type spin--pseudospin model, but in contrast to the usual version of the latter model, we are dealing here with the case of spin $S=1$ and pseudospin $1/2$. We show that the interplay of spin and pseudospin degrees of freedom leads to a rather nontrivial magnetic phase diagram including the spin-nematic configurations. Tuning the spin-channel interaction parameter $U_s$ gives rise to quantum phase transitions. We find that the ground state of the system always has the pseudospin domain structure. On the other hand, the sign change of $U_s$ switches the spin arrangement of the ground state within domains from ferro- to aniferromagnetic one. Finally, we revisit the spin (pseudospin)-1/2 Kugel--Khomskii model and see the inverse picture of phase transitions.