Entropy and specific heat of a critical quantum system with long-range interaction

Abstract

The entropy and the specific heat of a quantum spherical model with a long-range interaction (decreasing at large distances r as r–d–σ where d is the space dimensionality and 0 < σ ≤ 2) are studied in the quantum critical region at the upper quantum critical dimension d = 3σ/2. The problem of obtaining the temperature-dependent corrections to the ground state free energy involves the solution of a transcendental equation, the exact solution of which is expressed in terms of the Lambert W-function. The free energy, the entropy and the specific heat in the quantum critical region are derived in terms of the Lambert W-function. For systems in real physical dimensions (chains, thin layers, i.e. films and three-dimensional systems) the exact results for the entropy and the specific heat obtained in terms of the Lambert W-function and the leading asymptotic ones are compared on the basis of the calculated relative errors. It can be concluded that for a class of quantum models at the upper critical dimension the Lambert W-function is a very effective tool for an exact computation of low-temperature critical properties, especially in the finite-temperature quantum critical region.