Magnetic polarons in- and out-of equilibrium in strongly interacting antiferromagnets*

We develop a non-perturbative theoretical framework to describe the microscopic properties of magnetic polarons formed by holes hopping in an anti-ferromagnetic background on a square lattice. Based on the self-consistent Born approximation, we obtain a complete description of the polaron wave function by solving a set of Dyson-like equations that permit to compute relevant spin-hole correlation functions. We apply this new method to analyze the spatial structure of the magnetic polaron, which is shown to have a remarkably high symmetry and a surprising misalignment between its orientation and the crystal momentum. Our theory is then generalised to the out-of-equilibrium case, and we derive an expression for the time-dependent non-perturbative wave-function of the hole after it is initially created at a given lattice site. Using this wave function, we calculate the hole-dynamics and find excellent agreement with recent experimental results both for short and for long times. We end by discussing magnetic polarons in other lattice geometries.