Numerically Exact Generalized Green's Function Cluster Expansions for Electron-Phonon Problems

TL;DR

The paper introduces a numerically exact Green's function cluster expansion method that accurately computes particle-boson interactions across all regimes, including challenging adiabatic limits, for various models of charge-boson coupling.

Contribution

It develops the generalized Green's function cluster expansion (GGCE), an approximation-free, convergent hierarchy of equations for exact Green's function calculations in electron-phonon problems.

Findings

Successfully applied to Holstein and Peierls models.

Accessed exact results in the adiabatic limit.

Demonstrated systematic extension to complex models.

Abstract

We generalize the family of approximate momentum average methods to formulate a numerically exact, convergent hierarchy of equations whose solution provides an efficient algorithm to compute the Green's function of a particle dressed by bosons suitable in the entire parameter regime. We use this approach to extract ground-state properties and spectral functions. Our approximation-free framework, dubbed the generalized Green's function cluster expansion (GGCE), allows access to exact numerical results in the extreme adiabatic limit, where many standard methods struggle or completely fail. We showcase the performance of the method, specializing three important models of charge-boson coupling in solids and molecular complexes: the molecular Holstein model, which describes coupling between charge density and local distortions, the Peierls model, which describes modulation of charge hopping due to intersite distortions, and a more complex Holstein+Peierls system with couplings to two different phonon modes, paradigmatic of charge-lattice interactions in organic crystals. The GGCE serves as an efficient approach that can be systematically extended to different physical scenarios, thus providing a tool to model the frequency dependence of dressed particles in realistic settings.