Signatures of correlated magnetic phases in the local two-particle density matrix

Experiments with quantum gas microscopes have started to explore the antiferromagnetic phase of the two-dimensional Fermi-Hubbard model and effects of doping with holes away from half filling. In this work we show how direct measurements of the system averaged two-spin density matrix and its full counting statistics can be used to identify different correlated magnetic phases with or without long-range order. We discuss examples of phases which are potentially realized in the Hubbard model close to half filling, including antiferrromagnetically ordered insulators and metals, as well as insulating spin-liquids and metals with topological order. For these candidate states we predict the doping- and temperature dependence of local correlators, which can be directly measured in current experiments.Comment: 15 pages, 7 figure

Microscopic spinon-chargon theory of magnetic polarons in the t-J model

The interplay of spin and charge degrees of freedom, introduced by doping mobile holes into a Mott insulator with strong anti-ferromagnetic (AFM) correlations, is at the heart of strongly correlated matter such as high-Tc cuprate superconductors. Here we capture this interplay in the strong coupling regime and propose a trial wavefunction of mobile holes in an AFM. Our method provides a microscopic justification for a class of theories which describe doped holes moving in an AFM environment as meson-like bound states of spinons and chargons. We discuss a model of such bound states from the perspective of geometric strings, which describe a fluctuating lattice geometry introduced by the fast motion of the chargon. This is demonstrated to give rise to short-range hidden string order, signatures of which have recently been revealed by ultracold atom experiments. We present evidence for the existence of such short-range hidden string correlations also at zero temperature by performing numerical DMRG simulations. To test our microscopic approach, we calculate the ground state energy and dispersion relation of a hole in an AFM, as well as the magnetic polaron radius, and obtain good quantitative agreement with advanced numerical simulations at strong couplings. We discuss extensions of our analysis to systems without long range AFM order to systems with short-range magnetic correlations.Comment: 13 pages, 11 figure