Meson gas theory of the t-J model

We introduce a semi-variational theory for calculating the properties of holes in moderately doped t-J and related models. Our ansatz provides a microscopic description how holes form a confined pair of a spinon and a holon, connected by a geometric string of displaced spins. This resembles quarks constituting mesons in high-energy physics. We use our method to calculate how spin correlations change as a function of hole doping. Our results are benchmarked by comparison to experimental results from ultracold fermions in a quantum gas microscopes. In particular we show that a weakly correlated meson gas ansatz is sufficient for describing a broad range of dopings even at temperatures below J. Implications for the phase diagram of high-temperature superconductors, and the possibility of spin-charge separation, are also discussed.