Communications in Theoretical Physics

Quantum Phase Transitions in Anisotropic Spin Ladders with Antiferromagnetic Rungs

Qiang Gu, Shen JueLian

Published Jun 15, 1999• 0 citations

Abstract

We apply perturbation theory to study quantum phase transitions in anisotropic two-leg spin ladders with antiferromagnetic rungs in the strong interchain coupling limit. The energy gap is expanded up to the fourth order in the ratio of the intrachain to interchain couplings. The transition point is determined by examing the disappearance of the energy gap. Present results for the anisotropic ferromagnetic-leg spin ladder are consistent qualitatively with the nonlinear -model analysis and in good agreement with the numerical results by the diagonalization method.

DOI: 10.1088/0253-6102/31/4/631

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Communications in Theoretical Physics

Quantum Phase Transitions in Anisotropic Spin Ladders with Antiferromagnetic Rungs

Qiang Gu, Shen JueLian

Published Jun 15, 1999• 0 citations

Publisher

Abstract

DOI: 10.1088/0253-6102/31/4/631

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{J}^{z}{/J}^{\mathrm{xy}}.

It is found that the opening of the Haldane gap is qualitatively different for the two cases considered. For the two-leg ladder the Haldane gap opens for arbitrarily small interchain coupling, independent of

{J}^{z}{/J}^{\mathrm{xy}},

and the Haldane phase exists in a large region of parameter space. For the four-leg ladder the opening of the Haldane gap is strongly dependent on both the interchain coupling as well as

{J}^{z}{/J}^{\mathrm{xy}},

and the Haldane phase exists only in a narrow region about the isotropic antiferromagnet.

We investigate an

S=1/2

two-leg spin ladder with a cyclic four-spin exchange interaction whose interaction constant is denoted by

J_4

, by using the density matrix renormalization group method. The interchain and the intrachain interaction constant are denoted by

J_{rung}

and

J_{\rm leg}

, respectively and assumed to be antiferromagnetic. It turns out that a spin gap between the singlet (

S_{tot}^z=0

) and the triplet (

S_{tot}^z=1

) states vanishes at

J_4/J_{leg} \simeq 0.3

for

J_{rung}=J_{leg}

. This result is in contrast with the fact that the

S=1/2

antiferromagnetic Heisenberg ladder, that is the case of

J_{rung} \neq J_{leg}, J_4=0

, has a spin gap for all nonzero value of interchain interaction

J_{\rm rung}>0

. We find a larger value of the correlation length for the spin-pair correlation function than a linear size

L

of the system at

J_4/J_{\rm leg}=0.3

and

J_{rung}=J_{leg}

: the correlation length

ξ

is about 204 times of the lattice constant for L=84 for these values of interactions. We also find that the string correlation function decays rather algebraically than exponentially at

J_4/J_{leg}=0.3

and

J_{rung}=J_{leg}

. These results suggest that there is a quantum phase transition at

J_4/J_{leg} \simeq 0.3

for

J_{rung}=J_{leg}

. We estimate a phase boundary where the spin gap vanishes in a

J_4/J_{leg}-J_{rung}/J_{leg}

plane and obtain a consistent result with that by a perturbation theory for

J_{\rm rung}/J_{leg}>1