Abstract

The use of the single-particle Green’s function in quantum chemistry has become widespread as a result of its correspondence with the spectral function, allowing the study of a wide range of materials. I will present a method based on the block Lanczos approach that allows one to determine a Lehmann representation of the fully dynamic Green’s function, and associated self-energy, using only static expectation values in the form of the spectral moments. This recursion is, in principle, systematically improvable towards the limit of the fully dynamic functions, however suffers from numerical instability in the context of floating point arithmetic. Some results for classical quantum chemistry methods will show that this does not limit the usefulness of the approach, with acceptable errors attainable with few iterations of the recursion. The form of the moments of the Green’s function offer opportunities for their calculation using quantum algorithms, and doing so introduces a simple hybrid quantum-classical algorithm sufficient to calculate Green’s functions and self-energies on arbitrary quadrature.