Quasiparticle picture of topological phase transitions induced by interactions

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi mathvariant="double-struck">Z</a:mi><a:mn>2</a:mn></a:msub></a:math> 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.