Probing a quantum spin liquid with equilibrium and nonequilibrium hole dynamics

Abstract: The properties and experimental identification of quantum spin liquids (QSLs) remain an important topic with many fundamental questions. Here, we explore the dynamics of a single charge dopant (hole) in a $t$-$J_{1}$-$J_{2}$ model on a square lattice, which realizes a gapless $\mathbb{Z}_2$ QSL at half filling. Using a field theory approach based on the parton construction, which includes an infinite number of scatterings between the low-energy quasiparticle excitations of the QSL via a self-consistent Born approximation, we calculate both the equilibrium and nonequilibrium properties of the hole for weak and strong interactions. Quasiparticle branches as well as stringlike excitations of the holon are identified, and we furthermore explore the time-dependent spreading of a hole throughout the QSL after it has been injected at a given lattice site. The final ballistic expansion speed is shown to exhibit a nonmonotonic behavior as a quantum phase transition between an antiferromagnetic and the QSL phase is crossed, which is caused by a qualitative change in the fundamental kinematics of the interactions between the hole and the surrounding spins. Our results demonstrate how charge dopants can be used as a quantum probe for QSLs and are directly relevant to optical lattice experiments with single site resolution.