Slave boson

The slave boson method is a technique used to study strongly correlated electron systems by describing valence fluctuations within restricted state manifolds. Introduced by John Hubbard in the 1960s, the Hubbard operator was developed to describe electron creation in systems with strong Coulomb interactions, such as rare earth or actinide ions. These operators link quantum states of different valence configurations (e.g., Ce4+ and Ce3+) and form a graded Lie algebra with specific commutation relations.

In 1983, Piers Coleman extended this approach by introducing the slave boson formulation, which represented spinless and magnetic configurations using spinless "slave bosons" and Abrikosov slave fermions, respectively. This formulation preserved the graded Lie algebra of the Hubbard operators and allowed for field-theoretic treatments of valence fluctuations. The method was generalized to handle systems with larger irreducible representations of SU(2|1) by varying a conserved quantity \( Q \).

Further extensions of the slave boson approach included treating systems with multiple fermion components (\( N \)) and developing controlled large-\( N \) expansions. This framework has been widely applied in understanding strongly correlated systems, contributing to theories like the resonating valence bond (RVB) model of high-temperature superconductivity and advancing insights into heavy fermion compounds.