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Accueil du site > À la une > Spin gap and string order parameter in the ferromagnetic Spiral Staircase Heisenberg Ladder

Spin gap and string order parameter in the ferromagnetic Spiral Staircase Heisenberg Ladder

par Sylvain Capponi - 6 mars 2008

Low-dimensional quantum magnets are fascinating objects from both experimental and theoretical points of view. Spin-1/2 ladders have been widely studied and interpolate between the physics of one-dimensional antiferromagnetic (AF) spin chains and two-dimensional systems. In the one-dimensional (1D) case, there is an important mapping between spin-1/2 Heisenberg AF chains and Luttinger liquids which allows to treat such chains by means of exact fermionization and bosonization methods, resulting in a well-understood gapless phase. Coupling identical chains to form a spin ladder is however not a trivial task from a theoretical point of view. Indeed, the coupling is a relevant perturbation and, up to logarithmic corrections, opens a gap proportional to the interchain coupling.

We consider a spin-1/2 ladder with a ferromagnetic rung coupling $J_\bot$ and inequivalent chains (see figure).

This model is obtained by a twist ( $\theta$ ) deformation of the ladder and interpolates between the isotropic ladder ( $\theta=0$ ) and the ferromagnetic Kondo necklace model ( $\theta=\pi$ ). We show that the ground state in the ( $\theta$ , $J_\bot$ ) plane has a finite string order parameter characterising the Haldane phase.

This is expected in the strong coupling regime since, for large $J_\bot$ , the system effectively behaves a spin-1 Haldane chain. However, in the weak coupling case, recent theoretical studies (based on renormalization group techniques) have led to controversial results. Our large-scale numerical analysis confirm the persistence of the Haldane phase in the whole phase diagram.

Moreover, 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.

Post-scriptum :

For more details, see the original paper Spin gap and string order parameter in the ferromagnetic Spiral Staircase Heisenberg Ladder : a quantum Monte Carlo study, by C. Brünger, F. F. Assaad, S. Capponi, F. Alet, D. N. Aristov and M. N. Kiselev in Phys. Rev. Lett. 100, 017202 (2008) Selected for the Virtual Journal of Nanoscale Science & Technology, January 2008 Issue

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Spin gap and string order parameter in the ferromagnetic Spiral Staircase Heisenberg Ladder

Laboratoire de Physique Théorique
Toulouse - UMR 5152