arXiv:cond-mat/9608035 · Physical review. B, Condensed matter

Dynamics of the one-dimensional Heisenberg model and optical absorption of spinons in cuprate antiferromagnetic chains

J. Lorenzana, R. Eder

Published Feb 1, 1997• 52 citations

Abstract

We use numerical and analytical results to construct a simple ansatz for the energy dynamical correlation function of the one-dimensional antiferromagnetic Heisenberg model. This is applied to compute the phonon-assisted absorption spectra of magnetic excitations (spinons) in quasi-one-dimensional spin-1/2 insulators and shown to reproduce very well recent infrared measurements in ${\mathrm{Sr}}_{2}$ ${\mathrm{CuO}}_{3}$.

DOI: 10.1103/physrevb.55.r3358

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arXiv:cond-mat/9608035 · Physical review. B, Condensed matter

Dynamics of the one-dimensional Heisenberg model and optical absorption of spinons in cuprate antiferromagnetic chains

J. Lorenzana, R. Eder

Published Feb 1, 1997• 52 citations

arXiv HTML PDF

Abstract

{\mathrm{Sr}}_{2}

{\mathrm{CuO}}_{3}

DOI: 10.1103/physrevb.55.r3358

Related papers

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{\mathrm{Sr}}_{2}

{\mathrm{CuO}}_{3}

We use a high-statistic quantum Monte Carlo and maximum entropy regularization method to compute the dynamical energy correlation function (DECF) of the one-dimensional (1D)

S=1/2

antiferromagnetic Heisenberg model at finite temperatures. We also present a finite-temperature analytical ansatz for the DECF that is in very good agreement with the numerical data in the considered temperature range. From these results, and from a finite-temperature generalization of the mechanism proposed by Lorenzana and Sawatsky [Phys. Rev. Lett.

74,

1867 (1995)], we compute the line shape for the optical absorption spectra of multimagnon excitations assisted by phonons for quasi-1D compounds. The line shape has two contributions analogous to the Stokes and anti-Stokes process of Raman scattering. Our low-temperature data are in good agreement with optical absorption experiments of

{\mathrm{CuO}}_{3}

chains in

{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}.

Our finite-temperature results provide a nontrivial prediction on the dynamics of the Heisenberg model at finite temperatures that is easy to verify experimentally.

U/t

converging only slowly to the Heisenberg limit. We discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of

U/t

of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.

The

T=0

dynamical properties of the one-dimensional (1D)

s=\frac{1}{2}

Heisenberg antiferromagnet in a uniform magnetic field are studied via the Bethe ansatz for cyclic chains of N sites. The ground state at magnetization

0<{M}_{z}<N/2,

which can be interpreted as a state with

{2M}_{z}

spinons or as a state of $N/2\ensuremath{-}{M}_{z}$ magnons, is reconfigured here as the vacuum for a different species of quasiparticles, the psinons and antipsinons. We investigate three kinds of quantum fluctuations, namely the spin fluctuations parallel and perpendicular to the direction of the applied magnetic field and the dimer fluctuations. The dynamically dominant excitation spectra are found to be sets of collective excitations composed of two quasiparticles excited from the psinon vacuum in different configurations. The Bethe ansatz provides a framework for (i) the characterization of the new quasiparticles in relation to the more familiar spinons and magnons, (ii) the calculation of spectral boundaries and densities of states for each continuum, (iii) the calculation of transition rates between the ground state and the dynamically dominant collective excitations, (iv) the prediction of line shapes for dynamic structure factors relevant for experiments performed on a variety of quasi-1D antiferromagnetic compounds, including

{\mathrm{KCuF}}_{3},

\mathrm{Cu}({\mathrm{C}}_{4}{\mathrm{H}}_{4}{\mathrm{N}}_{2})({\mathrm{NO}}_{3}{)}_{2},

and

{\mathrm{CuGeO}}_{3}.

We employ spin-cluster perturbation theory to investigate the evolution of the spin excitation spectra of the mixed-dimensional antiferromagnetic

s=\frac{1}{2}

Heisenberg models from the one-dimensional chain to the two-dimensional square and honeycomb lattices by varying the spin interactions ${J}_{\ensuremath{\perp}}$ across the chains relative to ${J}_{\ensuremath{\parallel}}$ along the chains. In addition to the well-defined magnon excitations, the spectra of the N\'eel phases for both lattices exhibit anomalous high-energy continua that evolve continuously from the continuum of one-dimensional chain through increasing ${J}_{\ensuremath{\perp}}$. Notably, the key features of the continua at the two-dimensional limit for ${J}_{\ensuremath{\perp}}/{J}_{\ensuremath{\parallel}}=1$ are well consistent with experimental observations in real materials. Our results indicate that these high-energy continua in the N\'eel phases are a result of spinon deconfinement, which is further supported by a random-phase-approximation analysis based on the spinon Hubbard models.

\Gamma(\mathbf q=0)

and at the magnetic ordering wavevectors

\pm[\mathbf Q= (4\pi/3,0)]

, the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We have also investigated the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compares our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreements after the higher-order contributions are included in our calculations.