Three-Leg Antiferromagnetic Heisenberg Ladder with Frustrated Boundary Condition; Ground State Properties

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Abstract
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 ($J_{\perp}>0$). The estimated gap for the strong coupling limit ($J_{\perp}/J_1 \to \infty$) is 0.28$J_1$. 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.Comment: 15 pages, LaTeX, to be published in J.Phys.Soc.Jpn. Vol. 66 No. 1
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