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arXiv:1410.7828 · Physical Review A

$p$ orbitals in 3D lattices; fermions, bosons and (exotic) models of magnetism

Fernanda Pinheiro

Published Oct 28, 2014• 2 citations
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Abstract

We demonstrate how different types of $SU(3)$ Heisenberg models can be implemented with the use of the $p$ orbitals of three dimensional optical lattices. By considering a Mott insulator with unit filling, the dynamics is well described by an effective model derived from the perturbative treatment of the tunneling elements relative to the onsite interaction terms. This yields systems with degrees of freedom that are generators of the $SU(3)$ group, which extends the Heisenberg models frequently used to analyze quantum magnetism. Due to the different character of interactions in the bosonic and fermionic cases, the choice of atom determines what type of anisotropies will appear in the couplings of the corresponding effective Hamiltonians. Experimental schemes for detection and manipulation of these systems are presented, and properties of the ground states of selected examples are discussed.

DOI
10.48550/arxiv.1410.7828

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ppp orbitals in 3D lattices; fermions, bosons and (exotic) models of magnetism
We demonstrate how different types of SU(3)SU(3)SU(3) Heisenberg models can be implemented with the use of the ppp orbitals of three dimensional optical lattices. By considering a Mott insulator with unit filling, the dynamics is well described by an effective model derived from the perturbative treatment of the tunneling elements relative to the onsite interaction terms. This yields systems with degrees of freedom that are generators of the SU(3)SU(3)SU(3) group, which extends the Heisenberg models frequently used to analyze quantum magnetism. Due to the different character of interactions in the bosonic and fermionic cases, the choice of atom determines what type of anisotropies will appear in the couplings of the corresponding effective Hamiltonians. Experimental schemes for detection and manipulation of these systems are presented, and properties of the ground states of selected examples are discussed.
We study cold atoms in an optical lattice with synthetic spin-orbit coupling in the Mott-insulator regime. We calculate the parameters of the corresponding tight-binding model using Peierls substitution and "localized Wannier states method" and derive the low-energy spin Hamiltonian for bosons and fermions. The spin Hamiltonian is a combination of Heisenberg model, quantum compass model and Dzyaloshinskii-Moriya interactions and it has a rich classical phase diagram with collinear, spiral and vortex phases. We discuss the state of the art of experiments to realize and detect magnetic orderings in strongly correlated optical lattices.
We demonstrate how the spin-1/2 XYZ quantum Heisenberg model can be realized with bosonic atoms loaded in the p band of an optical lattice in the Mott regime. The combination of Bose statistics and the symmetry of the p-orbital wave functions leads to a nonintegrable Heisenberg model with antiferromagnetic couplings. Moreover, the sign and relative strength of the couplings characterizing the model are shown to be experimentally tunable. We display the rich phase diagram in the one-dimensional case and discuss finite size effects relevant for trapped systems. Finally, experimental issues related to preparation, manipulation, detection, and imperfections are considered.
Motivated by recent progress in the realization of artificial gauge fields and SU(NNN) Mott insulators using alkaline-earth-like atoms in optical lattices, we develop an unbiased SU(NNN) real-space dynamical mean-field theory approach to study the effect of spin-orbit coupling and on-site Hubbard interaction UUU on SU(3) fermionic systems. We investigate the behavior of the local magnetization, double occupancies, and the triple occupancy versus the Hubbard interaction across the metal to Mott insulator transition. We map out the magnetic phase diagram in the large-UUU limit and show that the spin-orbit coupling can stabilize long-range orders such as ferromagnets, spirals, and stripes with different orientations in SU(3) Mott insulators.
Strongly interacting fermionic atoms on optical lattices are studied through a Hubbard-like model Hamiltonian, in which tunneling rates of atoms and molecules between neighboring sites are assumed to be different. In the limit of large on-site repulsion UUU, the model is shown to reproduce the ttt-JJJ Hamiltonian, in which the JJJ coefficient of the Heisenberg term depends on the particle-assisted tunneling rate ggg: explicitly, J=4g2/UJ=4{g}^{2}/UJ=4g2/U. At half-filling, ggg drives a crossover from a Brinkman-Rice paramagnetic insulator of fully localized atoms (g=0g=0g=0) to the antiferromagnetic Mott insulator of the standard Hubbard case (g=tg=tg=t). This is observed already in the number of doubly occupied sites under the intermediate coupling regime, thus providing a criterion for extracting from measurements the effective value of ggg.
We study the Mott phase of three-component bosons, with one particle per site, in an optical lattice by mapping it onto an SU(3) spin model. In the simplest case of full SU(3) symmetry, one obtains a ferromagnetic Heisenberg model. Introducing an SU(3) analog of spin-orbit coupling, additional spin-spin interactions are generated. We first consider the scenario of spin-dependent hopping phases, leading to Dzyaloshinskii-Moriya-type interactions. They result in the formation of spiral spin textures, which in one dimension can be understood by a local unitary transformation. Applying classical Monte Carlo simulations, we extend our study to two-dimensional systems, and systems with ``true'' spin-orbit coupling, involving spin-changing hoppings.
We explore the properties of bosonic atoms loaded into the d bands of an isotropic square optical lattice. Following the recent experimental success reported in Zhai et al (2013 Phys. Rev. A 87 063638 ), in which populating d bands with a 99 fidelity was demonstrated, we present a theoretical study of the possible phases that can appear in this system. Using the Gutzwiller ansatz for the three d band orbitals we map the boundaries of the Mott insulating phases. For not too large occupation, two of the orbitals are predominantly occupied, while the third, of a slightly higher energy, remains almost unpopulated. In this regime, in the superfluid phase we find the formation of a vortex lattice, where the vortices come in vortex/anti-vortex pairs with two pairs locked to every site. Due to the orientation of the vortices time-reversal symmetry is spontaneously broken. This state also breaks a discrete -symmetry. We further derive an effective spin-1/2 model that describe the relevant physics of the lowest Mott-phase with unit filling. We argue that the corresponding two dimensional phase diagram should be rich with several different phases. We also explain how to generate anti-symmetric spin interactions that can give rise to novel effects like spin canting.