Spatial correlations in fermionic triangular lattice Hubbard systems*

Ultracold atoms in triangular optical lattices provide a versatile platform to study strongly correlated systems in which the interplay of motion, interactions and spin gives rise to new states of matter. The interesting feature for triangular lattices is the geometric frustration that three spins with antiferromagnetic interactions cannot be antiparallel, leading to large degeneracies in the many-body ground state [1]. The superposition of the degeneracies could result in a quantum spin liquid which is numerically predicted to occur between the metallic and ordered magnetic phases [2]. In this talk, we present a Mott insulator of lithium-6 on a symmetric triangular lattice with a lattice spacing of 1003 nm. The lattice is imaged using Raman sideband cooling technique with an imaging fidelity of 98% [3]. We calibrated tunneling and interaction by extracting lattice depth from band excitation. The temperature of our atoms is below one-fifth of the Fermi temperature before loading to the lattice and the temperature scale is less than the tunneling in the lattice. We performed spin removal technique [4] to resolve either spin up or down using on-resonance imaging light to detect spin-spin correlations. We compare the results to a numerical linked cluster expansion calculation and plan to investigate 120° Neel ordering in Heisenberg antiferromagnets and search for quantum spin liquids in the triangular lattice Hubbard system.

[1] L. Balents, Nature 464, 7286 (2010)

[2] M. Laubach, Phys. Rev. B 91, 245125 (2015)

[3] J. Yang, PRX Quantum 2, 020344 (2021)

[4] M. F. Parsons, Science 353, 1253-1256 (2016)