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arXiv:cond-mat/9807375 · Physical review. B, Condensed matter

Dynamical spin correlations in the Heisenberg ladder under a magnetic field and correlation functions in the SO(5) ladder

Akira Furusaki, Shoucheng Zhang

Published Jul 1, 1999• 61 citations
arXivHTMLPDF

Abstract

The zero-temperature dynamical spin-spin correlation functions are calculated for the spin-$\frac{1}{2}$ two-leg antiferromagnetic Heisenberg ladder in a magnetic field above the lower critical field ${H}_{c1}$. The dynamical structure factors are calculated, which exhibit both massless modes and massive excitations. These modes appear in different sectors characterized by the parity in the rung direction and by the momentum in the direction of the chains. The structure factors have power-law singularities at the lower edges of their support. The results are also applicable to the spin-1 Heisenberg chain. The implications are briefly discussed for the various correlation functions and the $\ensuremath{\pi}$ resonance in the SO(5) symmetric ladder model.

DOI
10.1103/physrevb.60.1175

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The zero-temperature dynamical spin-spin correlation functions are calculated for the spin-12\frac{1}{2}21​ two-leg antiferromagnetic Heisenberg ladder in a magnetic field above the lower critical field Hc1{H}_{c1}Hc1​. The dynamical structure factors are calculated, which exhibit both massless modes and massive excitations. These modes appear in different sectors characterized by the parity in the rung direction and by the momentum in the direction of the chains. The structure factors have power-law singularities at the lower edges of their support. The results are also applicable to the spin-1 Heisenberg chain. The implications are briefly discussed for the various correlation functions and the \ensuremathπ\ensuremath{\pi}\ensuremathπ resonance in the SO(5) symmetric ladder model.
We study the ground-state spin correlations in the gapless incommensurate regime of a S=1/2S=1/2S=1/2 XXZ\mathrm{XXZ}XXZ chain and a two-leg antiferromagnetic ladder under a magnetic field, in which the gapless excitations form a Tomonaga-Luttinger (TL) liquid. We calculate numerically the two-spin correlation functions and the local magnetization in the two models using the density-matrix renormalization-group method. By fitting the numerical results for an open XXZ\mathrm{XXZ}XXZ chain of 100 spins to correlation functions of a Gaussian model, we determine the TL-liquid parameter K and the amplitudes of the correlation functions. The value of K estimated from the fits is in excellent agreement with the exact value obtained from the Bethe ansatz. We apply the same method to the open ladder consisting of 200 spins and determine the dependence of K on the magnetization M. The $K\ensuremath{-}M$ relation changes drastically depending on the ratio of the coupling constants in the leg and rung directions. We also discuss implications of these results to experiments on the nuclear spin relaxation rate 1/T1{1/T}_{1}1/T1​ and dynamical spin structure factors.
We determine the dynamical structure factor of the two-leg spin-12\frac{1}{2}21​ Heisenberg ladder at low temperatures in the regime of strong rung coupling. The dominant feature at zero temperature is the coherent triplon mode. We show that the line shape of this mode broadens in a nonsymmetric way at finite temperatures and that the degree of asymmetry increases with temperature. We also show that at low frequencies, a temperature-induced resonance akin to the Villain mode in the spin-12\frac{1}{2}21​ Heisenberg Ising chain emerges.
We study the quantum critical behavior in the antiferromagnetic Heisenberg chain and two-leg Heisenberg ladder resulting from the application of an external magnetic field. In each of these systems a finite-temperature crossover line between two different ferromagnetic phases ends with a quantum critical point at zero temperature. Using the bond-mean-field theory, we calculate the field dependence of the magnetization and the mean-field spin bond parameters in both systems. For the Heisenberg chain, we recover the existing exact results and show in addition that the saturation of the zero-temperature magnetization at the field hc=2J{h}_{c}=2Jhc​=2J is accompanied by a quantum phase transition, where the bond parameter vanishes. Here JJJ is the exchange coupling constant along the chain. For the two-leg ladder, we also recover the known results, like the two magnetization plateaus, and show that at the upper critical field, which corresponds to the appearance of the saturation magnetization plateau, the chain and rung spin bond parameters vanish. The identification of the order parameters that govern the field-induced quantum criticality in the systems we study here constitutes an original contribution. Because no long-range order, which breaks symmetry, characterizes the bond order, the latter could be a proposal for the so-called hidden order. We calculate analytically the bond parameters in both systems as functions of the field in the low- and high-field limits at zero temperature. At nonzero temperatures, the calculation of the magnetization and bond parameters is carried out by solving the mean-field equations numerically.
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The critical properties of the S=1/2S=1/2S=1/2 Heisenberg two-leg ladders are investigated in a magnetic field. Combining the exact diagonalization method and the finite-size-scaling analysis based on conformal field theory, we calculate the critical exponents of spin correlation functions numerically. For a strong interchain coupling, magnetization dependence of the critical exponents shows characteristic behavior depending on the sign of the interchain coupling. We also calculate the critical exponents for the S=1/2S=1/2S=1/2 Heisenberg two-leg ladder with a diagonal interaction, which is thought of as a model Hamiltonian of the organic spin ladder compound ${\mathrm{Cu}}_{2}(1,4\ensuremath{-}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{z}\mathrm{a}\mathrm{c}\mathrm{y}\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{e}{)}_{2}{\mathrm{Cl}}_{4}.$ Numerical results are compared with experimental results of temperature dependence of the NMR relaxation rate 1/T1.{1/T}_{1}.1/T1​.