Generalized Chern numbers based on open system Green’s functions

• Published in: New journal of physics Vol. 23; no. 7; pp. 73009 - 73021
• Main Authors: Farias, M Belén, Groenendijk, Solofo, Schmidt, Thomas L
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01-07-2021
• Subjects: Eigenvectors; Energy; Hamiltonian functions; Integers; Measurement; non-Hermitian topological phases; Numbers; open quantum systems; Open systems; Physics; topological phases; Topology; two-dimensional quantum systems
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/ac0b04

We present an alternative approach to studying topology in open quantum systems, relying directly on Green’s functions and avoiding the need to construct an effective non-Hermitian (nH) Hamiltonian. We define an energy-dependent Chern number based on the eigenstates of the inverse Green’s function matrix of the system which contains, within the self-energy, all the information about the influence of the environment, interactions, gain or losses. We explicitly calculate this topological invariant for a system consisting of a single 2D Dirac cone and find that it is half-integer quantized when certain assumptions about the self-energy are made. Away from these conditions, which cannot or are not usually considered within the formalism of nH Hamiltonians, we find that such a quantization is usually lost and the Chern number vanishes, and that in special cases, it can change to integer quantization.