I will describe a non-perturbative analytic mapping framework that we recently developed in Ref. [1] to tackle the behavior of open quantum systems interacting with dissipative environments beyond the weak coupling limit. After presenting the method, I will discuss its applications to impurity and lattice models, touching on the transient [2] and the steady state limit [3]. In particular, I will focus on Ref. [4] where we systematically show how one can engineer different magnetic orders in spin systems by controlling the locality of the attached baths. I will discuss the following bath-induced transitions: (i) antiferromagnetic (AFM) to ferromagnetic ordering in a Heisenberg spin chain, (ii) AFM to an extended Neel phase order in the transverse-field Ising model, and (iii) a quantum phase transition in the fully connected Ising model. I will conclude with potential extensions to the mapping, e.g., to higher dimensions and to larger spin systems.

[4] B. Min, N. Anto-Sztrikacs, M. Brenes, and D. Segal, arXiv:2401.06227