Nonlinear Excitations and Coherent States in the Ising Model in a Transverse Field

Abstract

Nonlinear excitations in the Ising model in a transverse field or an equivalent Frenkel-exciton model for a system of two-level atoms are studied by using a method of diagonal coherent-state representation. It is shown that if the ratio of the Ising interaction to a transverse-field strength exceeds a certain critical value, stationary coherent states giving the ground state and excited states of the model Hamiltonian are characterized by two degenerate structures resulting from spatially uniform coherent states and static domain-wall type excitations, respectively. Particular solutions for the time evolution of spin operators corresponding to atomic polarization are then studied. It is shown that moving domain-wall solutions or moving solitary-wave solutions can exist under certain conditions.