Wigner-like expansion for the quantum-statistical mechanics of solids: Application to the sine-Gordon chain

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Abstract
A semiclassical expansion for the quantum partition function of solids is presented. With respect to the usual Wigner method, the temperature range where the expansion is significant is broadened owing to the correct quantum-statistical treatment of the harmonic modes, while a Wigner-like expansion is retained only for the anharmonic part. As an application, the lowest quantum correction to the specific heat of a one-dimensional sine-Gordon model is calculated analytically.