Wire deconstructionism of two-dimensional topological phases

Understand

A scheme is proposed to construct integer and fractional topological quantum states of fermions in two spatial dimensions.

• We devise models for such states by coupling wires of non-chiral Luttinger liquids of electrons, that are arranged in a periodic array.
• Which inter-wire couplings are allowed is dictated by symmetry and the compatibility criterion that they can simultaneously acquire a finite expectation value, opening a spectral gap between the ground state(s) and all excited states in the bulk.
• First, with these criteria at hand, we reproduce the tenfold classification table of integer topological insulators, where their stability against interactions becomes immediately transparent in the Luttinger liquid description.