A semiclassical trace formula for the canonical partition function of one dimensional systems

We present a semiclassical trace formula for the canonical partition function of arbitrary one-dimensional systems. The approximation is obtained via the stationary exponent method applied to the phase-space integration of the density operator in the coherent state representation. The formalism is valid in the low temperature limit, presenting accurate results in this regime. As illustrations we consider a quartic Hamiltonian that cannot be split into kinetic and potential parts, and a system with two local minima. Applications to spin systems are also presented.