Calculating Green Functions from Finite Systems

TL;DR

This paper compares different discretization schemes for calculating Green functions in finite quantum systems, emphasizing the importance of basis choice and boundary conditions for accurate spectral and dynamical results.

Contribution

It systematically evaluates various discretization methods, including Wilson NRG and damped boundary conditions, for impurity problems and their impact on spectral functions and wave packet evolution.

Findings

Logarithmic discretization improves spectral resolution at low energies.

Damped boundary conditions influence the time evolution of wave packets.

Choosing the right basis is crucial for accurate bulk spectral functions.

Abstract

In calculating Green functions for interacting quantum systems numerically one often has to resort to finite systems which introduces a finite size level spacing. In order to describe the limit of system size going to infinity correctly, one has to introduce an artificial broadening larger than the finite size level discretization. In this work we compare various discretization schemes for impurity problems, i.e. a small system coupled to leads. Starting from a naive linear discretization we will then discuss the logarithmic discretization of the Wilson NRG, compare it to damped boundary conditions and arbitrary discretization in energy space. We then discuss the importance of choosing the right single particle basis when calculating bulk spectral functions. Finally we show the influence of damped boundary conditions on the time evolution of wave packets leading to a NRG-tsunami.