Singularity structure analysis of the continuum Heisenberg spin chain with anisotropy and transverse field: Nonintegrability and chaos

The integrability aspects of the continuum limit of the one-dimensional anisotropic Heisenberg spin chain in a transverse magnetic field are studied by carrying out a Painlevé singularity structure analysis. The analytic structure of the system exhibits some unusual features and requires expansions that start like a Taylor series. A careful analysis exhibits the presence of a movable logarithmic critical singular manifold in the combined presence of the anisotropy and transverse field, thereby elucidating the nonintegrable nature. Numerical analysis on the static spin configurations of the nonintegrable case shows typically chaotic spatial structures.