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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. 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 vector of the model at a given site i {\displaystyle i} is n {\displaystyle \mathbf {n} }. Then, we can define rotor momentum p {\displaystyle \mathbf {p} } by the commutation relation of components α , β {\displaystyle \alpha ,\beta }
= i δ α β {\displaystyle =i\delta _{\alpha \beta }}