Quantum spin systems versus Schrodinger operators: A case study in spontaneous symmetry breaking

Spontaneous symmetry breaking (SSB) is mathematically tied to some limit, but must physically occur, approximately, before the limit. Approximate SSB has been independently understood for Schrodinger operators with double well potential in the classical limit [1, 2] and for quantum spin systems in the thermodynamic limit [3, 4]. We relate these to each other in the context of the Curie-Weiss model, establishing a remarkable relationship between this model (for finite N) and a discretized Schrodinger operator with double well potential.