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arXiv:1201.0844 · Journal of Physics Conference Series

Quasiparticles of string solutions in the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic field

Masanori Kohno

Published Jan 1, 2010• 3 citations
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Abstract

Spectral properties of the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic field are investigated by using exact Bethe-ansatz solutions. We argue that not only quasiparticles called psinon and antipsinon but also a quasiparticle representing a 2-string in the Bethe ansatz plays an important role for dynamical properties in a magnetic field. Combined with psinon and antipsinon, the quasiparticle for a 2-string forms a continuum in the high-energy regime for transverse dynamical structure factor S +− ( κ,ω ). In the zero-field limit, the continuum is located on the mode of the lowest excited states in zero field called the des Cloizeaux-Pearson mode. In a magnetic field, the continuum separates from other low-energy continua, and reduces to the mode of bound states of overturned spins from the fully polarized state near the saturation field. We confirm the relevance through comparisons with available experimental results on the quasi-one-dimensional antiferromagnet CuCl 2 ·2N(C 5 D 5 ).

DOI
10.1088/1742-6596/200/2/022027

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Bulletin of the American Physical Society•Mar 11, 2008•0 citations
Spectral properties of the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic field are investigated by using exact Bethe-ansatz solutions. We argue that not only quasiparticles called psinon and antipsinon but also a quasiparticle representing a 2-string in the Bethe ansatz plays an important role for dynamical properties in a magnetic field. Combined with psinon and antipsinon, the quasiparticle for a 2-string forms a continuum in the high-energy regime for transverse dynamical structure factor S +− ( κ,ω ). In the zero-field limit, the continuum is located on the mode of the lowest excited states in zero field called the des Cloizeaux-Pearson mode. In a magnetic field, the continuum separates from other low-energy continua, and reduces to the mode of bound states of overturned spins from the fully polarized state near the saturation field. We confirm the relevance through comparisons with available experimental results on the quasi-one-dimensional antiferromagnet CuCl 2 ·2N(C 5 D 5 ).
Using Bethe-ansatz solutions, this Letter uncovers a well-defined continuum in dynamical structure factor S+-(k,omega) of the spin-1/2 antiferromagnetic Heisenberg chain in magnetic fields. It comes from string solutions that continuously connect the mode of the lowest-energy excitations in the zero-field limit and that of bound states of overturned spins from the ferromagnetic state near the saturation field. The relevance to real materials is confirmed through comparisons with experimental results.
The T=0T=0T=0 dynamical properties of the one-dimensional (1D) s=12s=\frac{1}{2}s=21​ 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<Mz<N/2,0<{M}_{z}<N/2,0<Mz​<N/2, which can be interpreted as a state with 2Mz{2M}_{z}2Mz​ 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 KCuF3,{\mathrm{KCuF}}_{3},KCuF3​, Cu(C4H4N2)(NO3)2,\mathrm{Cu}({\mathrm{C}}_{4}{\mathrm{H}}_{4}{\mathrm{N}}_{2})({\mathrm{NO}}_{3}{)}_{2},Cu(C4​H4​N2​)(NO3​)2​, and CuGeO3.{\mathrm{CuGeO}}_{3}.CuGeO3​.
Recently there has been a renewed interest in the spectra and role in dynamical properties of excited states of the spin-1/2 Heisenberg antiferromagnetic chain in longitudinal magnetic fields associated with Bethe strings. The latter are bound states of elementary magnetic excitations described by Bethe-ansatz complex non-real rapidities. Previous studies on this problem referred to finite-size systems. Here we consider the thermodynamic limit and study it for the isotropic spin-1/2 Heisenberg XXX chain in a longitudinal magnetic field. We confirm that also in that limit the most significant spectral weight contribution from Bethe strings leads to (k,ω)-plane gapped continua in the spectra of the spin dynamical structure factors S+−(k,ω) and Sxx(k,ω)=Syy(k,ω). The contribution of Bethe strings to Szz(k,ω) is found to be small at low spin densities m and to become negligible upon increasing that density above m≈0.317. For S−+(k,ω), that contribution is found to be negligible at finite magnetic field. We derive analytical expressions for the line shapes of S+−(k,ω), Sxx(k,ω)=Syy(k,ω), and Szz(k,ω) valid in the (k,ω)-plane vicinity of singularities located at and just above the gapped lower thresholds of the Bethe-string states's spectra. As a side result and in order to provide an overall physical picture that includes the relative (k,ω)-plane location of all spectra with a significant amount of spectral weight, we revisit the general problem of the line-shape of the transverse and longitudinal spin dynamical structure factors at finite magnetic field and excitation energies in the (k,ω)-plane vicinity of other singularities. This includes those located at and just above the lower thresholds of the spectra that stem from excited states described by only real Bethe-ansatz rapidities.
We investigate spectral features of spatially anisotropic spin-1/2 frustrated antiferromagnets in a magnetic field by a weak-coupling approach from the one-dimensional (1D) limit. Using exact results of the Heisenberg chain, we calculate dynamical structure factors of spatially anisotropic frustrated antiferromagnets in two dimensions. We obtain rich peak structures depending on the momentum and the strength of magnetic fields. We identify the sharp peaks as bound and antibound states between particles carrying fractional Sz in 1D in a magnetic field, psinons and antipsinons, and those originating from 2-string solutions. We compare these spectral features with available experimental results on Cs2CuCl4, and suggest that the dynamical properties of Cs2CuCl4 in a magnetic field can be interpreted in terms of particles in 1D in a magnetic field.
The spin fluctuations parallel to the external magnetic field in the ground state of the one-dimensional (1D) s=12s=\frac{1}{2}s=21​ Heisenberg antiferromagnet are dominated by a two-parameter set of collective excitations. In a cyclic chain of N sites and magnetization 0<Mz<N/2,0<{M}_{z}<N/2,0<Mz​<N/2, the ground state, which contains 2Mz{2M}_{z}2Mz​ spinons, is reconfigured as the physical vacuum for a different species of quasiparticles, identifiable in the framework of the coordinate Bethe ansatz by characteristic configurations of Bethe quantum numbers. The dynamically dominant excitations are found to be scattering states of two such quasiparticles. For $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty},$ these collective excitations form a continuum in $(q,\ensuremath{\omega})$ space with an incommensurate soft mode. Their matrix elements in the dynamic spin structure factor ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ are calculated directly from the Bethe wave functions for finite N. The resulting line- shape predictions for $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ complement the exact results previously derived via algebraic analysis for the exact two-spinon part of ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ in the zero-field limit. They are relevant for neutron-scattering experiments on quasi-1D antiferromagnetic compounds in a strong magnetic field.
We investigate spectral features of spatially anisotropic spin-1/2 frustrated antiferromagnets in a magnetic field by a weak-coupling approach from the one-dimensional (1D) limit. Using exact results of the Heisenberg chain, we calculate dynamical structure factors of spatially anisotropic frustrated antiferromagnets in two dimensions. We obtain rich peak structures depending on the momentum and the strength of magnetic fields. We identify the sharp peaks as bound and antibound states between particles carrying fractional Sz in 1D in a magnetic field, psinons and antipsinons, and those originating from 2-string solutions. We compare these spectral features with available experimental results on Cs2CuCl4, and suggest that the dynamical properties of Cs2CuCl4 in a magnetic field can be interpreted in terms of particles in 1D in a magnetic field.