Thermodynamical observables in a finite temperature window from the Monte Carlo Hamiltonian

The Monte Carlo (MC) Hamiltonian is a new stochastic method to solve many-body problems. The MC Hamiltonian represents an effective Hamiltonian in a finite energy window. We construct it from the classical action via Monte Carlo with importance sampling. The MC Hamiltonian yields the energy spectrum and corresponding wave functions in a low energy window. This allows to compute thermodynamical observables in a low temperature window. We show the working of the MC Hamiltonian by an example from lattice field theory (Klein–Gordon model).