We use variational (VMC) and diffusion (DMC) Monte Carlo methods to study the ground state properties of boson or fermion fluids such as the He four or the Jellium. Through path integral Monte Carlo (PIMC) methods we determine the finite temperature properties (both in the canonical and in the grand-canonical ensembles). We study properties like the structure, the pressure, the internal energy, and various other thermodynamic quantities, the superfluid fraction, the fluid phase coexistence.

The Monte Carlo method is exact only for boson fluids. For fermion fluids, the yet unsolved "sign problem" requires the formulation of some approximation in the numerical calculation. So that even computationally we are still unable to extract exact statistical mechanical properties for fermions.

Nonetheless path integral Monte Carlo is able to describe both atoms and molecules formation from the soup of the constituent electrons and nuclei. This shows that the laws of quantum statistical physics and of Coulomb are enough to explain most of the matter we see around us.

In simulations of systems at room temperature or below and densities n such that T < T_F ∝ n^2/3ℏ²/m_ek_B, electrons are to a good approximation degenerate, and in most cases the nuclei can be treated as classical since m_p/m_e≅2000 where m_p is the proton mass and m_e the electron mass. In those cases, there exists an effective potential between the nuclei due to the electrons. Knowing this potential, one could solve most problems of chemical structure with simulation. But it needs to be computed very accurately because the natural electronic energy scale is the Hartree, m_ee⁴/ℏ², or Rydberg, e²/2a_B with a_B=ℏ²/m_ee² Bohr radius, and chemical energies are needed to better than k_BT. This requires an accuracy of one part in 10³ for a hydrogen atom. Higher relative accuracy is needed for heavier atoms. If T>T_F for fixed nuclei spatial positions it is necessary to perform a PIMC on the electrons component and use the result to perform a classical Monte Carlo (MC) calculation on the nuclei.