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Investigation of strongly interacting, nonlinear quantum field theories(QFT-s) remains one of the outstanding challenges of modern physics. Here, wedescribe analog quantum simulators for nonlinear QFT-s using mesoscopicsuperconducting circuit lattices. Using the Josephson effect as the source ofnonlinear interaction, we investigate generalizations of the quantumsine-Gordon model. In particular, we consider a two-field generalization, thedouble sine-Gordon model. In contrast to the sine-Gordon model, this model canbe purely quantum integrable, when it does not admit a semi-classicaldescription - a property that is generic to many multi-field QFT-s. The primarygoal of this work is to investigate different thermodynamic properties of thedouble sine-Gordon model and propose experiments that can capture its subtlequantum integrability. First, we analytically compute the mass-spectrum and theground state energy in the presence of an external `magnetic' field using Betheansatz and conformal perturbation theory. Second, we calculate thethermodynamic Bethe ansatz equations for the model and analyze its finitetemperature properties. Third, we propose experiments to verify the theoreticalpredictions.

Quantum Electronic Circuit Simulation of Generalized sine-Gordon Models