# Magnetic phases of orbital bipartite optical lattices

## TL;DR

This paper explores the rich magnetic phases arising from orbital hybridization in optical lattices, including classical and quantum frustrated states, and discusses the potential realization of quantum spin liquids in such systems.

## Contribution

It introduces a novel model for orbital bipartite optical lattices, analyzing magnetic phases and the possibility of quantum spin liquids using numerical and theoretical methods.

## Key findings

- Identification of various magnetic phases, including spin liquids and spin glasses.
- Mapping of the system to the $J_1$-$J_2$ model for Mott insulators.
- Demonstration of maximum frustration in the classical XY model.

## Abstract

In the Hamburg cold atom experiment with orbital states in an optical lattice, $s$- and $p$-orbital atomic states hybridize between neighbouring 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 neighbouring 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 $J_1$-$J_2$ model. Based on the knowledge of the $J_1$-$J_2$ model, together with numerical simulations, we discuss the possibility of realising 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 is expected to be a spin glass. Even with quantum fluctuations present it has been debated whether a spin liquid may persist at the point of full frustration.