Early experimental evidence of a topological quantum state: The signature of the Haldane ground state revealed by scattered neutrons

Neutron scattering played an important role in the experimental exploration of the theoretical ideas of Thouless, Haldane, and Kosterlitz, who won the Nobel Prize in Physics in 2016. This article reviews the signatures of Haldanes predicted topological quantum ground state and their observation in early neutron scattering experiments, which overturned the wisdom of the day.

Quantum Walks with Non-Orthogonal Position States

Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal. We develop a general description of such a quantum walk and show how to map it into a standard one with orthogonal states, thereby making available all the tools developed for the latter. This enables a variety of experiments, which can be implemented with smaller step sizes and more steps. Tuning the non-orthogonality allows for an easy preparation of extended states such as momentum eigenstates, which travel at a well-defined speed with low dispersion. We introduce a method to adjust their velocity by momentum shifts, which allows to investigate intriguing effects such as the analog of Bloch oscillations.

Reply to: Comment by S.-L. Drechsler et al. (arXiv:1006.5070v2)

In a comment on arXiv:1006.5070v2, Drechsler et al. claim that the frustrated ferromagnetic spin-1/2 chain LiCuVO4 should be described by a strong rather than weak ferromagnetic nearest-neighbor interaction, in contradiction with their previous work. Their comment is based on DMRG and ED calculations of the magnetization curve and the magnetic excitations. We show that their parameters are at odds with the magnetic susceptibility and the magnetic excitation spectrum, once intensities are taken into account, and that the magnetization curve cannot discriminate between largely different parameter sets within experimental uncertainties. We further show that their new exact diagonalization results support the validity of the RPA-approach, and strongly reinforce our conclusion on the existence of a four-spinon continuum in LiCuVO4, see Enderle et al., Phys. Rev. Lett. 104 (2010) 237207.

Reply to: Comment by S.-L. Drechsler et al. (arXiv:1006.5070v1)

In a comment on arXiv:1006.5070v1, Drechsler et al. present new band-structure calculations suggesting that the frustrated ferromagnetic spin-1/2 chain LiCuVO4 should be described by a strong rather than weak ferromagnetic nearest-neighbor interaction, in contradiction with their previous calculations. In our reply, we show that their new results are at odds with the observed magnetic structure, that their analysis of the static susceptibility neglects important contributions, and that their criticism of the spin-wave analysis of the bound-state dispersion is unfounded. We further show that their new exact diagonalization results reinforce our conclusion on the existence of a four-spinon continuum in LiCuVO4, see Enderle et al., Phys. Rev. Lett. 104 (2010) 237207.

Ferromagnetic Excitations in La$_{0.82}$Sr$_{0.18}$CoO$_{3}$ Observed Using Neutron Inelastic Scattering

Polarized neutron inelastic scattering has been used to measure spin excitations in ferromagnetic La$_{0.82}$Sr$_{0.18}$CoO$_{3}$. The magnon spectrum of these spin excitations is well defined at low energies but becomes heavily damped at higher energies, and can be modeled using a quadratic dispersion. We determined a spin wave stiffness constant of $D=94pm 3$,meV,AA$^{2}$. Assuming a nearest-neighbor Heisenberg model we find reasonable agreement between the exchange determined from D and the bulk Curie temperature. Several possible mechanisms to account for the observed spin-wave damping are discussed.

Excitations of the field-induced soliton lattice in CuGeO3

Here we report the first inelastic neutron scattering study of the magnetic excitations in the incommensurate phase of a spin-Peierls material. The results on CuGeO3 provide direct evidence of a finite excitation gap, two sharp magnetic excitation branches and a very low-lying excitation which is identified as a phason mode, the Goldstone mode of the incommensurate soliton lattice.

Neutron scattering study of the field-induced soliton lattice in CuGeO$_3$

CuGeO$_3$ undergoes a transition from a spin-Peierls phase to an incommensurate phase at a critical field of $H_capprox 12.5$ T. In the high-field phase a lattice of solitons forms, with both structural and magnetic components, and these have been studied using neutron scattering techniques. Our results provide direct evidence for a long-ranged magnetic soliton structure which has both staggered and uniform magnetizations, and with amplitudes that are broadly in accord with theoretical estimates. The magnetic soliton width, $Gamma$, and the field dependence of the incommensurability, $delta k_{sp}$, are found to agree well with theoretical predictions.