Path-integral Monte Carlo study of a model adsorbate with internal quantum states

An adsorbate in the strong-binding and small-corrugation limit is studied. The resulting two-dimensional fluid is treated in the adiabatic approximation: the translations of the particles are treated classically, whereas the internal quantum degrees of freedom are modeled by interacting two-state tunneling systems. The temperature-coverage phase diagram is obtained to a high degree of precision by combining finite-size-scaling ideas with path-integral Monte Carlo techniques. Even this simplified adsorbate model possesses a surprisingly complex phase diagram including first- and second-order transitions as well as a tricritical and a triple point. We identify gas, liquid, fluid, and square-lattice solid phases combined with a preferred internal quantum state depending on temperature and coverage. We determine the order of the transitions and localize the different phase boundaries of this many-body quantum system reliably. Mean-field approximations and low-density expansions are compared to the simulations. A possible extension of the block analysis method to determine triple points and solid coexistence densities is discussed.