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

An Approach to Loop Quantum Cosmology Through Integrable Discrete Heisenberg Spin Chains