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

Kenro Kawano; Minoru Takahashi

doi:10.1143/JPSJ.66.4001

paper

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

arXiv:cond-mat/9709271 · doi:10.1143/JPSJ.66.4001

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 ( $J_{⊥} > 0$ ). The estimated gap for the strong coupling limit ( $J_{⊥} / J_{1} \to \infty$ ) 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.

15 pages, LaTeX, to be published in J.Phys.Soc.Jpn. Vol. 66 No. 12

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

Abstract

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