Nonequilibrium Hole Dynamics in Antiferromagnets: Damped Strings and Polarons

TL;DR

This paper presents a nonperturbative theoretical framework for understanding the nonequilibrium dynamics of holes in antiferromagnets, revealing regimes of string excitation and polaron formation consistent with cold-atom experiments.

Contribution

It generalizes the selfconsistent Born approximation to nonequilibrium systems, enabling full time-dependent wave function calculations in the $t$-$J$ model.

Findings

Identification of three dynamical regimes in hole motion.

Observation of oscillations due to string excitations.

Formation of magnetic polarons with reduced velocity.

Abstract

We develop a nonperturbative theory for hole dynamics in antiferromagnetic spin lattices, as described by the $t$-$J$ model. This is achieved by generalizing the selfconsistent Born approximation to nonequilibrium systems, making it possible to calculate the full time-dependent many-body wave function. Our approach reveals three distinct dynamical regimes, ultimately leading to the formation of magnetic polarons. Following the initial ballistic stage of the hole dynamics, coherent formation of string excitations gives rise to characteristic oscillations in the hole density. Their damping eventually leaves behind magnetic polarons that undergo ballistic motion with a greatly reduced velocity. The developed theory provides a rigorous framework for understanding nonequilibrium physics of defects in quantum magnets and quantitatively explains recent observations from cold-atom quantum simulations in the strong coupling regime.