The Recursion Method

Application to Many-Body Dynamics



V. S. Viswanath and Gerhard Müller

Lecture Notes in Physics m23
Springer-Verlag New York 1994
ISBN 3-540-58319-X    (259pp.)

In this monograph the recursion method is presented and employed as a method for the analysis of dynamical properties of quantum and classical many-body systems in thermal equilibrium. Such properties are probed as the linear response to a time-dependent external field by many experimental techniques used in materials science.

Several representations and formulations of the recursion method are described in great detail and documented with numerous examples. They range from elementary illustrations for tutorial purposes to relalistic models of interest in current research in the areas of spin dynamics and low-dimensional magnetism. The performance of the recursion method is calibrated by exact results in a number of benchmark tests and compared with the performance of other calculational techniques in several applications.

In zero-temperature applications, the continued-fraction analysis presented in this book extracts the following kinds of quantitative information from a given finite-size ground-state wave function: (i) type of ordering in the system, (ii) gaps in dynamically relevant excitation spectra, (iii) infrared singularities, bandwidths, and line shapes of spectral densities.

Table of Contents

Section 1-1