Z_2-slave-spin theory for strongly correlated fermions

Understand

We review a representation of Hubbard-like models that is based on auxiliary pseudospin variables.

• These pseudospins refer to the local charge modulo two in the original model and display a local Z_2 gauge freedom.
• We discuss the associated mean-field theory in a variety of different contexts which are related to the problem of the interaction-driven metal-insulator transition at half-filling including Fermi surface deformation and spectral features beyond the local approximation.
• Notably, on the mean-field level, the Hubbard bands are derived from the excitations of an Ising model in a transverse field and the quantum critical point of this model is identified with the Brinkman-Rice criticality of the almost localized Fermi liquid state.