Path integral approach to the thermodynamics of anharmonic phonons

A new kind of effective potential, which permits the calculation of the quantum partition function in classical-like way, is introduced, as well as a related effective potential, which permits to compute equilibrium averages of configuration dependent observables. A low-coupling expansion is derived in the general case, which makes possible the use of the method for ordered many-body systems. The main feature of these effective potentials is the capability to fully account for the quantum harmonic effects, so they prove much more efficient than the analogous one defined by the Wigner expansion. This framework is used for calculating the quantum pair correlation function of a two-body system and the free energy of a chain of atoms with nearest-neighbor interaction. Application with the Lennard-Jones potential is made and explicit results are shown. Our technique based on the effective potential offers an alternative to the quantum Monte Carlo approach.