Gap's in the antiferromagnetic Heisenberg model

Abstract

We study the one-dimensional spin-1/2 antiferromagnetic Heisenberg model exposed to an external field, which is a superposition of a homogeneous field $h_3$ and a small periodic field of strength $h_1$. For the case of a transverse staggered field a gap opens, which scales with $h_1^{{\epsilon }_1}$, where ${\epsilon }_1={\epsilon }_1(h_3)$ is given by the critical exponent ${\eta }_1(M(h_3))$ defined through the transverse structure factor of the model at $h_1=0$. For the case of a longitudinal periodic field with wave vector $q=\pi /2$ and strength $h_q$ a plateau is found in the magnetization curve at $M=1/4$. The difference of the upper- and lower magnetic field scales with $h_3^u-h_3^l\sim h_q^{{\epsilon }_3}$, where ${\epsilon }_3={\epsilon }_3(h_3)$ is given by the critical exponent ${\eta }_3(M(h_3))$ defined through the longitudinal structure factor of the model at $h_q=0$.

7 pages, 6 figures, LaTeX-class svjour from Springer; to be published in Eur. Phys. J. B