Mathematics Colloquia and Seminars

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In 1928, Heisenberg presented a model for describing ferromagnetism based on the interaction of electron spins and studied the ground states and low energy excitations. In 1940, Holstein and Primakoff showed that the Heisenberg Hamiltonian can be rewritten in terms of bosonic creation and annihilation operators. In this new form, the Heisenberg Hamiltonian looks very similar to the second quantized Laplacian in a low-temperature high spin limit. In a recent paper, Correggi, Giuliani, and Seiringer proved that this approximation correctly calculates the free energy in the low-temperature limit for fixed spin. In this talk, I will give an introduction to the quantum spin systems and bosonic systems and outline the proof.