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We show that LiVCuO4 should be described by strongly ferromagnetically coupled Heisenberg antiferromagnetic chains (HAC) in sharp contrast with the effective exchange integrals Ji given in Enderle et al., Phys. Rev. Lett. vol. 104, 237207 (2010), and the main issues of that work, namely, (i) LiVCuO4 is well described by two weakly ferromagnetically coupled interpenetrating Heisenberg antiferromagnetic spin-1/2 chains, (ii) the extracted exchange integrals J1, J2 agree with a previous spin-wave description (Enderle et al., Euphys. Lett. vol. 70, 237 (2005)), (iii) the spectral density of inelastic neutron scattering (INS) above 10 meV is ascribed to a 4-spinon continuum. Applying exact diagonalization and DMRG methods to fit their INS and magnetization M(H) data, supported by two independent microscopic methods (5-band Hubbard model and LSDA+U calculations), we demonstrate that LiCuVO4 exhibits strong inchain frustration with alpha =-J2/J1 < 1, i.e. strong coupling of the HAC at odds with (i). An alternative phenomenological set in accord with various experimental results is proposed. In view of the recent possible discovery of quantum-spin nematics and Bose condensation of two-magnon bound states (M. Zhitomirsky et al. arXiv:1003.4096v2 (2010), L. Svistov et al. ibid. 1005.5668v2 (2010)) in LiCuVO4 precise knowledge of the main J-values is of key importance.
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We explain how spinons and magnons naturally arise in $mathrm{SU}(2)$ invariant spin chains when describing ground states and elementary excitations using MPS. Within this description, spinons can emerge in a spin-1 chain at a first-order transition between a symmetry-protected topological phase and a trivial phase. We provide MPS simulations for the spinon dispersion relations in a frustrated and dimerized spin-1 chain, and show that these spinons determine the low-lying spectrum in the vicinity of this transition by the formation of spinon/anti-spinon bound states.
One-dimensional (1D) magnetic insulators have attracted significant interest as a platform for studying emergent phenomena such as quasiparticle fractionalization and quantum criticality. The antiferromagnetic Heisenberg chain of spins-1/2 is an important reference system; its elementary excitations are spin-1/2 quasiparticles called spinons that are always created in pairs. However, while inelastic neutron scattering (INS) experiments routinely observe the excitation continuum associated with two-spinon states, the presence of more complex dynamics associated with four-spinon states has only been inferred from comparison with theory. Here, we show that resonant inelastic x-ray scattering (RIXS) is capable of accessing the four-spinon excitations directly, in a spectroscopic region separated from the two-spinon continuum. Our results provide the first direct measurement of four-spinon excitations, which is made possible by the fundamentally different correlation functions probed by RIXS compared to INS. This advance holds great promise as a tool in the search for novel quantum states, in particular quantum spin liquids.
Elementary excitations of the S=1/2 one-dimensional antiferromagnet KCuGaF_6 were investigated by inelastic neutron scattering in zero and finite magnetic fields perpendicular to the (1, 1, 0) plane combined with specific heat measurements. KCuGaF$_6$ exhibits no long-range magnetic ordering down to 50 mK despite the large exchange interaction J/k_B=103 K. At zero magnetic field, well-defined spinon excitations were observed. The energy of the des Cloizeaux and Pearson mode of the spinon excitations is somewhat larger than that calculated with the above exchange constant. This discrepancy is mostly ascribed to the effective XY anisotropy arising from the large Dzyaloshinsky-Moriya interaction with an alternating D vector. KCuGaF_6 in a magnetic field is represented by the quantum sine-Gordon model, for which low-energy elementary excitations are composed of solitons, antisolitons and their bound states called breathers. Unlike the theoretical prediction, it was found that the energy of a soliton is smaller than that of the first breather, although the energy of the first breather coincides with that observed in a previous ESR measurement.
We have investigated the thermal conductivity kappa_mag of high-purity single crystals of the spin chain compound Sr2CuO3 which is considered an excellent realization of the one-dimensional spin-1/2 antiferromagnetic Heisenberg model. We find that the spinon heat conductivity kappa_mag is strongly enhanced as compared to previous results obtained on samples with lower chemical purity. The analysis of kappa_mag allows to compute the spinon mean free path l_mag as a function of temperature. At low-temperature we find l_magsim0.5mum, corresponding to more than 1200 chain unit cells. Upon increasing the temperature, the mean free path decreases strongly and approaches an exponential decay ~1/T*exp(T*/T) which is characteristic for umklapp processes with the energy scale k_B T*. Based on Matthiesens rule we decompose l_mag into a temperature-independent spinon-defect scattering length l0 and a temperature dependent spinon-phonon scattering length l_sp(T). By comparing l_mag(T) of Sr2CuO3 with that of SrCuO2, we show that the spin-phonon interaction, as expressed by l_sp is practically the same in both systems. The comparison of the empirically derived l_sp with model calculations for the spin-phonon interaction of the one-dimensional spin-1/2 XY model yields reasonable agreement with the experimental data.
We study the interplay of competing interactions in spin-$1/2$ triangular Heisenberg model through tuning the first- ($J_1$), second- ($J_2$), and third-neighbor ($J_3$) couplings. Based on large-scale density matrix renormalization group calculation, we identify a quantum phase diagram of the system and discover a new {it gapless} chiral spin liquid (CSL) phase in the intermediate $J_2$ and $J_3$ regime. This CSL state spontaneously breaks time-reversal symmetry with finite scalar chiral order, and it has gapless excitations implied by a vanishing spin triplet gap and a finite central charge on the cylinder. Moreover, the central charge grows rapidly with the cylinder circumference, indicating emergent spinon Fermi surfaces. To understand the numerical results we propose a parton mean-field spin liquid state, the $U(1)$ staggered flux state, which breaks time-reversal symmetry with chiral edge modes by adding a Chern insulator mass to Dirac spinons in the $U(1)$ Dirac spin liquid. This state also breaks lattice rotational symmetries and possesses two spinon Fermi surfaces driven by nonzero $J_2$ and $J_3$, which naturally explains the numerical results. To our knowledge, this is the first example of a gapless CSL state with coexisting spinon Fermi surfaces and chiral edge states, demonstrating the rich family of novel phases emergent from competing interactions in triangular-lattice magnets.
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