Thermodynamics and spin gap of the Heisenberg ladder calculated by the look-ahead Lanczos algorithm

TL;DR

This paper introduces an improved quantum transfer matrix algorithm using the look-ahead Lanczos method to efficiently compute thermodynamic properties and spin gaps in the Heisenberg ladder model.

Contribution

An advanced algorithm combining the look-ahead Lanczos method with quantum transfer matrices for accurate eigenvalue calculations in non-Hermitian systems.

Findings

Confirmed the existence of a spin gap of about 0.5 J in the Heisenberg ladder.

Calculated temperature-dependent susceptibility, specific heat, and correlation length.

Demonstrated higher efficiency and accuracy over traditional methods.

Abstract

We have developed an improved version of the quantum transfer matrix algorithm. The extreme eigenvalues and eigenvectors of the transfer matrix are calculated by the recently developed look-ahead Lanczos algorithm for non-Hermitian matrices with higher efficiency and accuracy than by the power method. We have applied this method to the Heisenberg ladder. The temperature dependence of the susceptibility, specific heat, correlation length and nuclear spin relaxation rate $1/T_1$ are calculated. Our results support the existence of a spin gap of about $0.5 J$. The preprint is submitted as a uuencoded compressed PostScript file. In case of printing problems the original TeX file (without figures) can be retrieved by anonymous ftp to 'maggia.ethz.ch' filename 'CSSP/preprints/hblad.tex'. Alternatively from June 1, 1994 by WWW: URL "http://www.ips.id.ethz.ch/CSSP/preprints.html"