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We present an exact analytical solution for quantum strong long-range modelsin the canonical ensemble by extending the classical solution proposed in[Campa et al., J. Phys. A 36, 6897 (2003)]. Specifically, we utilize theequivalence between generalized Dicke models and interacting quantum models asa generalization of the Hubbard-Stratonovich transformation. To demonstrate ourmethod, we apply it to the Ising chain in transverse field and discuss itspotential application to other models, such as the Fermi-Hubbard model,combined short and long-range models and models with antiferromagneticinteractions. Our findings indicate that the critical behaviour of a model isindependent of the range of interactions, within the strong long-range regime,and the dimensionality of the model. Moreover, we show that the order parameterexpression is equivalent to that provided by mean-field theory, thus confirmingthe exactness of the latter. Finally, we examine the algebraic decay ofcorrelations and characterize its dependence on the range of interactions inthe full phase diagram.

Exact solution for quantum strong long-range models via a generalized Hubbard-Stratonovich transformation