Broken symmetry

Ground states that choose less symmetry than their Hamiltonian — order parameters, rigidity, and Goldstone modes.

Every topic that illustrates this idea, drawn from across all subjects.

• Weak Coupling: Mean-Field Theory and the Slater Insulator Mott Physics in Correlated Lattices Starting from the non-interacting limit, a mean-field decoupling of the Hubbard interaction with staggered magnetization gives an antiferromagnetic two-band insulator. Solving the self-consistent gap equation reveals a Slater gap that opens exponentially at weak coupling and crosses over to the Mott gap Δ → U/2 at strong coupling.
• Strong Coupling: Perturbation Theory and Superexchange Mott Physics in Correlated Lattices In the opposite limit U ≫ t, treating hopping as a perturbation and projecting out doubly occupied sites with a Schrieffer–Wolff transformation maps the half-filled Hubbard model onto the antiferromagnetic Heisenberg model, with superexchange J = 4t²/U.