Three-leg antiferromagnetic Heisenberg ladder with frustrated boundary condition; Ground state properties

The antiferromagnetic Heisenberg spin systems on the three-leg ladder are investigated. Periodic boundary condition is imposed in the rung direction. The system has an excitation gap for all antiferromagnetic inter-chain coupling (J(perpendicular to) > 0). The estimated gap for the strong coupling limit (J(perpendicular to)/J(1)--> infinity) is 0.28J(1). Although the interaction is homogeneous and only nearest-neighbor, the ground states of the system are dimerized and break the translational symmetry in the thermodynamic limit. Introducing the next-nearest neighbor coupling (J(2)), We can see that the system is solved exactly. The ground state wave function is completely dimer-ordered. Using density matrix renomalization group algorithm, we show numerically that the original model (J(2) = 0) has the same nature with the exactly solvable model. The ground state properties of the ladder with a higher odd number of legs are also discussed.