Transfer-matrix renormalization group study of the spin ladders with cyclic four-spin interactions

TL;DR

This study uses the transfer-matrix renormalization group method to analyze how cyclic four-spin interactions affect the thermodynamic properties of spin ladders, revealing linear relationships and magnon dispersion characteristics.

Contribution

It introduces a detailed numerical analysis of spin ladders with cyclic four-spin interactions using TMRG, highlighting the linear dependence of the spin gap and magnon dispersion.

Findings

Spin gap is approximately linear with cyclic four-spin interaction.

Magnon branch dispersion can be numerically fitted from the partition function.

Thermodynamic properties depend on the relative strength of interactions.

Abstract

The temperature dependence of the specific heat and spin susceptibility of the spin ladders with cyclic four-spin interactions in the rung-singlet phase is explored by making use of the transfer-matrix renormalization group method. The values of spin gap are extracted from the specific heat and susceptibility, respectively. It is found that for different relative strength between interchain and intrachain interactions, the spin gap is approximately linear with the cyclic four-spin interaction in the region far away from the critical point. Furthermore, we show that the dispersion for the one-triplet magnon branch can be obtained by numerically fitting on the partition function.