Dynamical Spin Response Functions for Heisenberg Ladders

TL;DR

This paper numerically investigates the dynamical spin response of a 2 by L Heisenberg ladder, providing detailed energy gap data and analyzing the effectiveness of moments techniques for response calculations.

Contribution

It introduces a numerical approach combining Lanczos and moments techniques to study spin response functions in Heisenberg ladders, with validation against previous results.

Findings

Ground state energies and gaps for L=4 to 14 are obtained.

Dynamical spin response functions are evaluated for L=12 across various interaction ratios.

Discussion on reorthogonalization and convergence issues in moments method.

Abstract

We present the results of a numerical study of the 2 by L spin 1/2 Heisenberg ladder. Ground state energies and the singlet-triplet energy gaps for L = (4-14) and equal rung and leg interaction strengths were obtained in a Lanczos calculation and checked against earlier calculations by Barnes et al. (even L up to 12). A related moments technique is then employed to evaluate the dynamical spin response for L=12 and a range of rung to leg interaction strength ratios (0 - 5). We comment on two issues, the need for reorthogonalization and the rate of convergence, that affect the numerical utility of the moments treatment of response functions.