Quantum rotor model

rdf:langString Quantum rotor model

rdf:langString The quantum rotor model is a mathematical model for a quantum system. It can be visualized as an array of rotating electrons which behave as rigid rotors that interact through short-range dipole-dipole magnetic forces originating from their magnetic dipole moments (neglecting Coulomb forces). The model differs from similar spin-models such as the Ising model and the Heisenberg model in that it includes a term analogous to kinetic energy. Although elementary quantum rotors do not exist in nature, the model can describe effective degrees of freedom for a system of sufficiently small number of closely coupled electrons in low-energy states. Suppose the n-dimensional position (orientation) vector of the model at a given site is . Then, we can define rotor momentum by the commutation relation of components However, it is found convenient to use rotor angular momentum operators defined (in 3 dimensions) by components Then, the magnetic interactions between the quantum rotors, and thus their energy states, can be described by the following Hamiltonian: where are constants.. The interaction sum is taken over nearest neighbors, as indicated by the angle brackets. For very small and very large , the Hamiltonian predicts two distinct configurations (ground states), namely "magnetically" ordered rotors and disordered or "paramagnetic" rotors, respectively. The interactions between the quantum rotors can be described by another (equivalent) Hamiltonian, which treats the rotors not as magnetic moments but as local electric currents.