  A novel approach for studying phase transitions in systems with quantum
degrees of freedom is discussed. Starting from the microscopic hamiltonian of a
quantum model, we first derive a set of exact differential equations for the
free energy and the correlation functions describing the effects of
fluctuations on the thermodynamics of the system. These equations reproduce the
full renormalization group structure in the neighborhood of a critical point
keeping, at the same time, full information on the non universal properties of
the model. As a concrete application we investigate the phase diagram of a
Heisenberg antiferromagnet in a staggered external magnetic field. At long
wavelengths the known relationship to the Quantum Non Linear Sigma Model
naturally emerges from our approach. By representing the two point function in
an approximate analytical form, we obtain a closed partial differential
equation which is then solved numerically. The results in three dimensions are
in good agreement with available Quantum Monte Carlo simulations and series
expansions. More refined approximations to the general framework presented here
and few applications to other models are briefly discussed.
