The Bosonic RKKY Effect: Long-Range Order in a Spin-Boson Chain

Coupling of a two-level system to a dissipative bosonic bath is a well-studied problem known as the Caldeira-Leggett model. Here, we generalize this model to a 1D chain of Ising pseudospins coupled to a bosonic bath with Ohmic dissipation. Bath-induced interactions can produce a long-range ordered state even in the absence of direct interactions between the pseudospins. By analogy to the RKKY effect in metal-impurity systems, we refer to these induced interactions as the "Bosonic RKKY Effect". The long-range interactions depend on the form of the bath boson spectral function, which must be chosen based on the physical implementation. For a bath spectral function that decays exponentially above the cutoff frequency ω_c, the bosonic RKKY interactions drive a quantum phase transition from a quantum paramagnet to a quantum Ising ferromagnet as the dissipation strength increases. By employing a quantum-to-classical mapping [1], we use classical Monte Carlo simulations to study the quantum phase diagram of the spin-boson chain. We find that the universality class of this quantum critical point is distinct from previously studied related models.

References:
[1] S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 1999).