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Progress of Theoretical Physics Supplement

Half Plateau Phase Diagram in Generalized Zig-Zag Spin Ladder

Akiyuki Tokuno, Kiyomi Okamoto, Takashi Tonegawa

Published Jan 1, 2005• 1 citation
Publisher

Abstract

We study the finite-field ground state of an anisotropic S = 1/2 antiferromagnetic chain with bond-alternating nearest-neighbor and uniform next-nearest-neighbor interactions. The ground-state magnetization curve of this model has a plateau at a half of the saturation magnetization in a certain parameter region. We analytically investigate the plateau phase of this model by use of the degenerate perturbation theory up to the second order.

DOI
10.1143/ptps.159.265

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We study the finite-field ground state of an anisotropic S = 1/2 antiferromagnetic chain with bond-alternating nearest-neighbor and uniform next-nearest-neighbor interactions. The ground-state magnetization curve of this model has a plateau at a half of the saturation magnetization in a certain parameter region. We analytically investigate the plateau phase of this model by use of the degenerate perturbation theory up to the second order.
We numerically investigate the magnetization process of a frustrated S =1 chain with antiferromagnetic nearest-neighbor (nn) and next-nearest-neighbor (nnn) exchange interactions, which compete with each other, and also with uniaxial single-ion-type anisotropy energies. Special attention is paid to the half magnetization plateau which appears at the half of the saturation magnetization in the ground-state magnetization curve. We determine the parameter region where this plateau appears by employing the level spectroscopy method, and find that the plateau appears even in the absence of the single-ion-type anisotropy, if the ratio of the nnn to the nn interaction constant is in a specified region.
The magnetization process of the S=1/2 antiferromagnetic spin ladder at T=0 is studied by the exact diagonalization of finite clusters and size scaling analyses. It is found that a magnetization plateau appears at half the saturation value (m=1/2) in the presence of a sufficiently large next-nearest-neighbor exchange interaction to yield the frustration, when the rung coupling is larger than the leg one. The phase diagram at m=1/2 is given by the analysis based on the conformal invariance. The magnetization curves are also presented in several cases.
We have studied the ground state phase diagram of a spin ladder with alternating rung exchange J⊥n=J⊥[1+(−1)nδ]J^{n}_{\perp} = J_{\perp}[1 + (-1)^{n} δ]J⊥n​=J⊥​[1+(−1)nδ] in a magnetic filed, in the limit where the rung coupling is dominant. In this limit the model is mapped onto an XXZXXZXXZ Heisenberg chain in a uniform and staggered longitudinal magnetic fields, where the amplitude of the staggered field is ∼δ\sim δ∼δ. We have shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. The width of a plateau scales as δνδ^νδν, where ν=4/5ν=4/5ν=4/5 in the case of ladder with isotropic antiferromagnetic legs and ν=2ν=2ν=2 in the case of ladder with isotropic ferromagnetic legs. We have calculated four critical fields (Hc1±H^{\pm}_{c1}Hc1±​ and Hc2±H^{\pm}_{c2}Hc2±​) corresponding to transitions between different magnetic phases of the system. We have shown that these transitions belong to the universality class of the commensurate-incommensurate transition.
We analyze the phase diagram of a system of spin-1/2 Heisenberg antiferromagnetic chains interacting through a zig-zag coupling, also called zig-zag ladders. Using bosonization techniques we study how a spin-gap or more generally plateaux in magnetization curves arise in different situations. While for coupled XXZ chains, one has to deal with a recently discovered chiral perturbation, the coupling term which is present for normal ladders is restored by an external magnetic field, dimerization or the presence of charge carriers. We then proceed with a numerical investigation of the phase diagram of two coupled Heisenberg chains in the presence of a magnetic field. Unusual behaviour is found for ferromagnetic coupled antiferromagnetic chains. Finally, for three (and more) legs one can choose different inequivalent types of coupling between the chains. We find that the three-leg ladder can exhibit a spin-gap and/or non-trivial plateaux in the magnetization curve whose appearance strongly depends on the choice of coupling.
We study the S =1/2 and S =1 alternating spin Heisenberg chain with the next-nearest neighbor (NNN) interaction J 2 between neighboring S =1/2 spins, by using the numerical diagonalization method of a finite size system. It is found that a fractional plateau appears at magnetization m =1/2 in the magnetization curve for J 2 > J 2 c =0.106±0.001. The phase transition at J 2 c is characterized by the exponent σ=1, which controls the critical behavior of the spin gap Δ as Δ∼ exp(- a /( J 2 - J 2 c ) 1+σ ). For J 2 < J 2 c , the model at m =1/2 is described by the conformal field theory with central charge c =1 and exponent η for the spin correlation function of the transverse component to a magnetic field is calculated.
We study the magnetization plateau at m =1/2 in the S =1/2 and S =1 alternating spin Heisenberg chain with two next-nearest-neighbor (NNN) interactions J a between neighboring S =1/2 spins and J b between neighboring S =1 spins, using the numerical diagonalization and the density-matrix renormalization group (DMRG) method. We present the m =1/2 plateau phase diagram in the J a – J b plane obtained by the level crossing method useful for the Berezinskii–Kosterlitz–Thouless (BKT) transition. In this phase diagram, we find that there are two plateau phases distinguished by a parity of the alternating spin chain.