Properties of the one-particle density matrix in an interacting Chern insulator

The notion of a topological insulator is rooted in the physics of non-interacting
particles but generalizes to interacting systems. Here we investigate how much
of the topological properties of an interacting Chern insulator is encoded in
the single--particle quantities derived from the single-particle density matrix (OPDM)
computed in the many-body ground state. The diagonalization of the OPDM
yields the occupation spectrum and its eigenfunctions. In a concrete example,
we study how the occupations evolve as a function of interactions and how the
eigenfunctions are deformed away from the non-interacting limit. After resolving
potential ambiguities in defining OPDM eigenbands, we compute the Chern numbers
for these emergent OPDM bands, which are necessarily quantized. The behavior of these
quantities, occupations, OPDM eigenfunctions, and OPDM Chern numbers, across a
transition into a topologically trivial phase is discussed. We finally discuss the
connection between the OPDM and topological invariants derived from single-particle
Green's functions.