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We describe a family of lattice models that support a new class of quantummagnetism characterized by correlated spin and bosonic ordering [Phys. Rev.Lett. 112, 180405 (2014)]. We explore the full phase diagram of the model usingMatrix-Product-State methods. Guided by these numerical results, we describe amodified variational ansatz to improve our analytic description of thegroundstate at low boson frequencies. Additionally, we introduce anexperimental protocol capable of inferring the low-energy excitations of thesystem by means of Fano scattering spectroscopy. Finally, we discuss theimplementation and characterization of this model with current circuit-QEDtechnology.

The Interspersed Spin Boson Lattice Model