arXiv:cond-mat/9508098 · Journal of the Physical Society of Japan

Hidden Orders and RVB Formation of the Four-Leg Heisenberg Ladder Model

Yoshihiro Nishiyama, Naomichi Hatano, Masuo Suzuki

Published Feb 15, 1996• 9 citations

Abstract

The ground state of the four-chain Heisenberg ladder model is numerically investigated. Hidden-order correlations suitable for the system are introduced and calculated with an emphasis on the spatially isotropic point, where a corresponding material exists. The existence of a long-range hidden correlation indicates formation of a short-range RVB state in the case of the antiferromagnetic inter-chain coupling. A transition between the phase of the ferromagnetic inter-chain coupling and that of the antiferromagnetic one is discussed.

DOI: 10.1143/jpsj.65.560

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arXiv:cond-mat/9508098 · Journal of the Physical Society of Japan

Hidden Orders and RVB Formation of the Four-Leg Heisenberg Ladder Model

Yoshihiro Nishiyama, Naomichi Hatano, Masuo Suzuki

Published Feb 15, 1996• 9 citations

arXiv HTML PDF

Abstract

DOI: 10.1143/jpsj.65.560

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c=2.

The critical value of ${J}_{\ifmmode\times\else\texttimes\fi{}}$ is insensitive to the number of legs in the ladder, suggesting that a quantum phase transition may occur at ${J}_{\ifmmode\times\else\texttimes\fi{}}=0.6$ for the isotropic spin-1/2 antiferromagnetic Heisenberg model on the square lattice.

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.

Dimerized antiferromagnetic spin-

\frac{1}{2}

ladders are known to exhibit a quantum critical phase transition in the ground state, the existence or absence of which is dependent on the dimerization pattern of the ladder. The gapped phases cannot be distinguished by the conventional Landau long-range order parameter. However, they possess a nonlocal (hidden) string-order parameter, which is nonzero in one phase and vanishes in the other. We use an exact diagonalization technique to calculate ground-state energies, energy gaps, and string-order parameters of dimerized two- and three-leg Heisenberg ladders, as well as a critical scaling analysis to yield estimates of the critical exponents $\ensuremath{\nu}$ and $\ensuremath{\beta}$.