Quasiparticle picture of topological phase transitions induced by interactions

Abstract: We present a general recipe to describe topological phase transitions in condensed matter systems with interactions. We show that topological invariants in the presence of interactions can be efficiently calculated by means of a non-Hermitian quasiparticle Hamiltonian introduced on the basis of the Green's function. As an example analytically illustrating the application of the quasiparticle concept, we consider a topological phase transition induced by the short-range electrostatic disorder in a two dimensional system described by the Bernevig-Hughes-Zhang model. The latter allows us to explicitly demonstrate the change in the $\mathbb{Z}_2$ topological invariant and explain the quantized values of the longitudinal conductance in a certain range of the Fermi energy and the disorder strength found previously in numerical calculations.