Densities of States, Moments, and Maximally Broken Time-Reversal Symmetry

TL;DR

This paper develops a method to approximate densities of states with macroscopic limits by constraining moments with minimal lifetimes and broken time-reversal symmetry, improving upon traditional continued fraction expansions.

Contribution

It introduces a novel approach to the moment problem by incorporating physical constraints, enabling more accurate density of states approximations in complex models.

Findings

Effective approximation of densities of states with macroscopic limits.

Comparison shows improved accuracy over maximum entropy methods.

Applicable to models with finite and infinite bands.

Abstract

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 point-wise 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 band-width, and the results are compared with the maximum entropy approximation where possible.