We simulate spectral functions for electron-phonon coupling in a filled band
system - far from the asymptotic limit often assumed where the phonon energy is
very small compared to the Fermi energy in a parabolic band and the Migdal
theorem predicting 1+lambda quasiparticle renormalizations is valid. These
spectral functions are examined over a wide range of parameter space through
techniques often used in angle-resolved photoemission spectroscopy (ARPES).
Analyzing over 1200 simulations we consider variations of the microscopic
coupling strength, phonon energy and dimensionality for two models: a
momentum-independent Holstein model, and momentum-dependent coupling to a
breathing mode phonon. In this limit we find that any `effective coupling',
lambda_eff, inferred from the quasiparticle renormalizations differs from the
microscopic dimensionless coupling characterizing these Hamiltonians, lambda,
and could drastically either over- or under-estimate it depending on the
particular parameters and model. In contrast, we show that perturbation theory
retains good predictive power for low coupling and small momenta, and that the
momentum-dependence of the self-energy can be revealed via the relationship
between velocity renormalization and quasiparticle strength. Additionally we
find that (although not strictly valid) it is often possible to infer the
self-energy and bare electronic structure through a self-consistent
Kramers-Kronig bare-band fitting; and also that through lineshape alone, when
Lorentzian, it is possible to reliably extract the shape of the imaginary part
of a momentum-dependent self-energy without reference to the bare-band.Comment: 15 pages, 11 figures. High resolution available here:
http://www.physics.ubc.ca/~quantmat/ARPES/PUBLICATIONS/Articles/sf_tour.pd