Spin gap and string order parameter in the ferromagnetic Spiral Staircase Heisenberg Ladder: a quantum Monte Carlo study

TL;DR

This study uses quantum Monte Carlo simulations to explore a deformed ferromagnetic spin ladder, revealing a Haldane phase with a finite string order parameter and a crossover in the spin gap scaling influenced by chain twisting.

Contribution

It introduces a twist deformation in a ferromagnetic ladder model and analyzes its effects on the ground state and spin gap scaling using large-scale quantum Monte Carlo methods.

Findings

Identification of a Haldane phase with string order parameter

Observation of a crossover in spin gap scaling at a critical twist angle

Demonstration of the impact of chain twisting on energy scales and interactions

Abstract

We consider a spin-1/2 ladder with a ferromagnetic rung coupling J_\perp and inequivalent chains. This model is obtained by a twist (\theta) deformation of the ladder and interpolates between the isotropic ladder (\theta=0) and the SU(2) ferromagnetic Kondo necklace model (\theta=\pi). We show that the ground state in the (\theta,J_\perp) plane has a finite string order parameter characterising the Haldane phase. Twisting the chain introduces a new energy scale, which we interpret in terms of a Suhl-Nakamura interaction. As a consequence we observe a crossover in the scaling of the spin gap at weak coupling from \Delta/J_\| \propto J_\perp/J_\| for \theta < \theta_c \simeq 8\pi/9 to \Delta/J_\| \propto (J_\perp/J_\|)^2 for \theta > \theta_c. Those results are obtained on the basis of large scale Quantum Monte Carlo calculations.