PATH-INTEGRAL MONTE-CARLO STUDY OF A MODEL 2-DIMENSIONAL QUANTUM PARAELECTRIC

We have started a study of quantum ferroelectrics and paraelectrics. Simple two-dimensional short-range lattice model Hamiltonians are constructed, keeping in mind the phenomenology of real perovskite systems, like SrTiO3 and KTaO3. Pertinent quantum tunneling phenomena, and the presence of an icelike constraint are demonstrated. The two simplest models, namely a plain quantum four-state clock model and a constrained one, are then studied in some detail. We show the equivalence of the former, but not of the latter, to a quantum Ising model. For the latter, we describe a very good analytical wave function valid in the special case of zero coupling (J = 0). In order to study the full quantum statistical mechanics of these models, a path-integral Monte Carlo calculation is set up, and implemented with a technique, which even in the constrained case permits a good convergence for increasing time slice number m. The method is applied first to the unconstrained model, which serves as a check, and successively to the constrained quantum four-state clock model. It is found that in both cases a quantum phase transition at T = 0 takes place at finite coupling J, between a ferroelectric and a quantum paraelectric state, even when the constraint hinders disordering of the ferroelectric state. These model paraelectric states have a finite excitation gap, and no broken symmetry. The possible role of additional (''oxygen hopping'') kinetic terms in making closer contact with the known phenomenology of SrTiO3 is proposed.