Magnetic phases of orbital bipartite optical lattices

Abstract

In the Hamburg cold atom experiment with orbital states in an optical lattice, s- and p-orbital atomic states hybridize between neighboring sites. In this work we show how this alternation of sites hosting s- and p-orbital states gives rise to a plethora of different magnetic phases, quantum and classical. We focus on phases whose properties derive from frustration originating from a competition between nearest and next nearest neighboring exchange interactions. The physics of the Mott insulating phase with unit filling is described by an effective spin-1/2 Hamiltonian showing great similarities with the J1–J2 model. Based on the knowledge of the J1–J2 model, supported by numerical simulations, we discuss the possibility of a quantum spin liquid phase in the present optical lattice system. In the superfluid regime we consider the parameter regime where the s-orbital states can be adiabatically eliminated to give an effective model for the p-orbital atoms. At the mean-field level we derive a generalized classical XY model, and show that it may support maximum frustration. When quantum fluctuations can be disregarded, the ground state should be a spin glass.