Bath-Induced Interactions in a One-Dimensional Dissipative Spin Chain

The spin-boson model has been widely studied for its rich physics and potential for controlling entangled quantum states. In this context, we consider a one-dimensional chain of quantum spins which are coupled to a common dissipative bath, which can be realized in ultra-cold atomic mixtures of Bose-Fermi gases trapped in an optical lattice. This "multiple spin boson model" has been studied for spins with effectively zero spatial separation [1], but the case of many, finitely-separated spins has not been previously investigated due to algorithmic difficulties. When the spins are finitely separated, the bath induces long-range, frustrated spin-spin interactions in both space and imaginary time. To study the effects of these induced interactions, we employ a quantum-to-classical mapping [2] to derive the action of the corresponding classical Ising model in two dimensions. We investigate the spin localization and spatial ordering in this model with classical Monte Carlo simulations, using parallel tempering and cluster update algorithms to mitigate the difficulties of dealing with a highly frustrated spin system.
References:
[1] A. Winter, H. Rieger, Phys. Rev. B, 90, 224401 (2014).
[2] S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 1999).