Ground state properties of chiral XY-model on a one-dimensional lattice

We investigate ground state properties of a chiral XY-model on a one-dimensional lattice in which we have two parameters: natural cantedness α and field strength γ. We perform numerical calculations for the ground state energy and periodic configurations. We get the energy, its derivative in terms of α, the magnetization and the devil's staircase as functions of α for γ=0.2 and the energy and the magnetization as functions of γ for α⧸2π=320. We obtain the phase diagram in the parameter space (α, γ). An area-preserving map, which is obtained from the stationary condition for the energy, is numerically investigated in relation to periodic orbits giving the minimum energy. The exact solutions for the energy and periodic orbits are given for winding numbers 0, case14 and case16.