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A way of constructing continuous matrix product states (cMPS) for coupledfields is presented here. The cMPS is a variational \emph{ansatz} for theground state of quantum field theories in one dimension. Our proposed scheme isbased in the physical interpretation in which the cMPS class can be produced bymeans of a dissipative dynamic of a system interacting with a bath. We studythe case of coupled bosonic fields. We test the method with previous DMRGresults in coupled Lieb Liniger models. Besides, we discuss a novel applicationfor characterizing the Luttinger liquid theory emerging in the low energyregime of these theories. Finally, we propose a circuit QED architecture as aquantum simulator for coupled fields.

Continuous matrix product states for coupled fields: Application to Luttinger Liquids and quantum simulators