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

We have started a study of quantum ferroelectrics and paraelectrics. S imple two-dimensional short-range lattice model Hamiltonians are const ructed, 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 m odels, 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 latte r, we describe a very good analytical wave function valid in the speci al case of zero coupling (J = 0). In order to study the full quantum s tatistical mechanics of these models, a path-integral Monte Carlo calc ulation 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, whi ch serves as a check, and successively to the constrained quantum four -state clock model. It is found that in both cases a quantum phase tra nsition at T = 0 takes place at finite coupling J, between a ferroelec tric and a quantum paraelectric state, even when the constraint hinder s disordering of the ferroelectric state. These model paraelectric sta tes have a finite excitation gap, and no broken symmetry. The possible role of additional (''oxygen hopping'') kinetic terms in making close r contact with the known phenomenology of SrTiO3 is proposed.