Quantum gases in trimerized kagom\'e lattices

TL;DR

This paper explores the low-temperature behavior of atomic gases in trimerized kagomé lattices, revealing a quantum spin-liquid crystal state with unique magnetic properties and discussing experimental verification methods.

Contribution

It introduces a detailed analysis of atomic gases in trimerized kagomé lattices, including Hubbard model parameters and the discovery of a novel quantum spin-liquid crystal phase.

Findings

Existence of a Mott insulator phase with fractional particles per trimer.

Identification of a quantum spin-liquid crystal with antiferromagnetic order and many low-energy excitations.

Couplings in the effective spin model depend on bond directions, affecting magnetic properties.

Abstract

We study low temperature properties of atomic gases in trimerized optical kagom\'{e} lattices. The laser arrangements that can be used to create these lattices are briefly described. We also present explicit results for the coupling constants of the generalized Hubbard models that can be realized in such lattices. In the case of a single component Bose gas the existence of a Mott insulator phase with fractional numbers of particles per trimer is verified in a mean field approach. The main emphasis of the paper is on an atomic spinless interacting Fermi gas in the trimerized kagom\'{e} lattice with two fermions per site. This system is shown to be described by a quantum spin 1/2 model on the triangular lattice with couplings that depend on the bond directions. We investigate this model by means of exact diagonalization. Our key finding is that the system exhibits non-standard properties of a quantum spin-liquid crystal: it combines planar antiferromagnetic order in the ground state with an exceptionally large number of low energy excitations. The possibilities of experimental verification of our theoretical results are critically discussed.