Meson formation in a mixed-dimensional t-J model

In this paper, we study a mixed-dimensional version of the t-J model. While the anti-ferromagnetic spin-exchange interactions extend in two dimensions, additionally doped holes can only move along one direction. We explain how this model can be implemented using ultracold fermions in optical lattices.

We study the properties of a single hole and find strong indications for the formation of mesons: the hole can be understood as a composite of a chargon (or holon) and a spinon, both fractions of a physical fermion, much like pairs of quarks binding to form a meson in high-energy physics. We provide a microscopic theory of the spinon-chargon binding, which can be tested in a quantum gas microscope by analyzing higher-order correlation functions.