Domain walls in the quantum transverse Ising model.

We discuss several problems concerning domain walls in the spin-S Ising model at zero temeprature in a magnetic field, H/(2S), applied in the x direction. Some results are also given for the planar (y-z) model in a transverse field. We treat the quantum problem in one dimension by perturbation theory at small H and numerically over a large range of H. We obtain the spin-density profile by fixing the spins at opposite ends of the chain to have opposite signs of Sz. One dimensional is special in that there the quantum width of the wall is proportional to the size L of the system. We also study the quantitative features of the "particle" band which extends up to energies of order H above the ground state. Except for the planar limit, this particle band is well separated from excitations having energy J/S involving creation of more walls. At large S this particle band develops energy gaps and the lowest subband has tunnel splittings of order H21−2S. This scale of of energy gives rise to anomalous scaling with respect to (a) finite size, (b) temperature, or (c) random potentials. The intrinsic width of the domain wall and the pinning energy are also defined and calculated in certain limiting cases. The general conclusion is that quantum effects prevent the wall from being sharp and in higher dimension would prevent sudden excursions in the configuration of the wall. Disciplines Physics | Quantum Physics Comments At the time of publication, author A. Brooks Harris was also affiliated with Oxford University, Oxford, United Kingdom. Currently, he is a faculty member in the Physics Department at the University of Pennsylvania. This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/350 PHYSICAL REVIEW B VOLUME 52, NUMBER 6 1 AUGUS'I 1995-II Domain walls in the quantum transverse Ising model Malte Henkel Theoretical Physics, Ozford University, 1 Keble Road, Ozford OX1 8NP, United Kingdom A. Brooks Harris Theoretical Physics, Ozford University, 1 Keble Road, Ozford OX1 8NP, United Kingdom and Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6896 Marek Cieplak Institute of Physics, Polish Academy of Sciences, 02-668 Warsazv, Poland (Received 21 February 1995; revised manuscript received 25 April 1995) We discuss several problems concerning domain walls in the spin-S Ising model at zero temperature in a magnetic field, H/(2S), applied in the z direction. Some results are also given for the planar (y-z) model in a transverse field. We treat the quantum problem in one dimension by perturbation theory at small H and numerically over a large range of H. We obtain the spin-density profile by fixing the spins at opposite ends of the chain to have opposite signs of S . One dimension is special in that there the quantum width of the wall is proportional to the size L of the system. We also study the quantitative features of the "particle" band which extends up to energies of order H above the ground state. Except for the planar limit, this particle band is well separated from excitations having energy J/S involving creation of more walls. At large S this particle band develops energy gaps and the lowest subband has tunnel splittings of order H2 . This scale of energy gives rise to anomalous scaling with respect to (a) finite size, (b) temperature, or (c) random potentials. The intrinsic width of the domain wall and the pinning energy are also defined and calculated in certain limiting cases. The general conclusion is that quantum eKects prevent the wall from being sharp and in higher dimension would prevent sudden excursions in the configuration of the wall.