Densities of states, moments, and maximally broken time-reversal symmetry

Power moments, modified moments, and optimized moments are powerful tools for solving microscopic models of macroscopic systems; however, the expansion of the density of states as a continued fraction does not converge to the macroscopic limit point-wise in energy with increasing numbers of moments. In this work the moment problem is further constrained by minimal lifetimes or maximal breaking of time-reversal symmetry, to yield approximate densities of states with pointwise macroscopic limits. This is applied numerically to models with one and two finite bands with various singularities, as well as to a model with infinite bandwidth, and the results are compared with the maximum entropy approximation where possible.