  The quantum evolution equation of Loop Quantum Cosmology (LQC) -- the quantum
Hamiltonian constraint -- is a difference equation. We relate the LQC
constraint equation in vacuum Bianchi I separable (locally rotationally
symmetric) models with an integrable differential-difference nonlinear
Schr\"odinger type equation, which in turn is known to be associated with
integrable, discrete Heisenberg spin chain models in condensed matter physics.
We illustrate the similarity between both systems with a simple constraint in
the linear regime.
