Speaker
Description
The electron Green's function is a powerful tool that describes single-particle excitations in correlated systems, commonly associated with poles in the complex frequency plane. Intriguingly, when strong interactions come into play, the Green's function determinant can also have bands of zeros, corresponding to poles of the self-energy. However, these zeros have long been for long overlooked and considered incidental to the formalism without carrying any physical significance.
In spite of that, these zeroes do possess a topological character. Indeed, we show that when the thermal Green’s function is invertible, nor poles neither zeros at zero Matsubara frequency, thus representing a bona fide insulator, the two-dimensional quantized Hall conductance, which is a topological invariant, is equally contributed by bands of poles and bands of zeros. This result is exact and fully non-perturbative, insofar the Luttinger-Ward functional of the Green’s functions can be defined non-perturbatively, as rigorously shown, whose first functional derivative yields the self-energy, and second functional derivative the irreducible scattering vertex. This result, which we believe is readily extendable in higher dimensions and for other topological invariants, brings to light the importance of the Green’s functions band of zeros, especially in Mott topological insulators.
