Classification of spin liquids

A paper in need to understand better is a 2002 PRB by Wen.

Wen used quantum orders and projective symmetry groups, to construct hundreds of symmetric spin liquids, having either SU(2), U(1), or Z2 gauge structures at low energies. He divided the spin liquids into four classes:

(a) Rigid spin liquid—spinons (and all other excitations) are fully gapped and may have bosonic, fermionic, or fractional statistics.

(b) Fermi spin liquid—spinons are gapless and are described by a Fermi liquid theory (i.e, the interaction between quasiparticles on the Fermi surface vanishes.)

(c) Algebraic spin liquid—spinons are gapless, but they are not described by free fermionic-bosonic quasiparticles.

(d) Bose spin liquid—low-lying gapless excitations are described by a free-boson theory.