  The properties of mobile impurities in quantum magnets are fundamental for
our understanding of strongly correlated materials and may play a key role in
the physics of high-temperature superconductivity. Hereby, the motion of
hole-like defects through an antiferromagnet has been of particular importance.
It creates magnetic frustrations that lead to the formation of a quasiparticle,
whose complex structure continues to pose substantial challenges to theory and
numerical simulations. In this article, we develop a non-perturbative
theoretical approach to describe the microscopic properties of such magnetic
polarons. Based on the self-consistent Born approximation, which is provenly
accurate in the strong-coupling regime, 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 magnetic polarons in the strongly interacting
regime and find qualitative differences from predictions of previously applied
truncation schemes. Our calculations reveal a remarkably high spatial symmetry
of the polaronic magnetization cloud and a surprising misalignment between its
orientation and the polaron crystal momentum. The developed framework opens up
an approach to the microscopic properties of doped quantum magnets and will
enable detailed analyses of ongoing experiments based on cold-atom quantum
simulations of the Fermi-Hubbard model.

Strongly Correlated Electrons;Quantum Gases