The interplay between spin and orbital degrees of freedom gives rise to a variety of emergent phases in correlated $4d$ and $5d$ transition-metal systems. Among these materials, it is known that strong spin–orbit coupling (SOC) significantly alters Jahn-Teller (JT) effects, either by suppressing static distortions or promoting dynamic fluctuations, so that orbital polarization related to JT effects is reduced or even quenched. Here, by using a Matsubara lattice formalism, we investigate how orbital fluctuations are generated and propagated by local perturbations in spin-orbit coupled systems with no global polarization, corresponding to either orbitally disordered phases or dynamic JT regimes. By analyzing how such perturbations propagate through the correlated, spin-orbit-entangled ground state, we observe that they generate short-range orbital fluctuations that carry local polarization. We find that these dynamical fluctuations propagate to neighboring sites with a polarization orthogonal to the initial perturbation. Finally, we discuss to what extent such orbital fluctuations may be probed as excitations in spectroscopic measurements.

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• Exotic phases of matter
• Jahn-Teller effect
• Spin-orbit coupling
• Strongly correlated systems
• Approximation methods for many-body systems
• Finite temperature field theory
• Green's function methods
• Lattice models in condensed matter
• Second quantization
• Tight-binding model