The 4-spinon dynamical structure factor of the Heisenberg chain

We compute the exact 4-spinon contribution to the zero-temperature dynamical structure factor of the spin-1/2 Heisenberg isotropic antiferromagnet in zero magnetic field, directly in the thermodynamic limit. We make use of the expressions for matrix elements of local spin operators obtained by Jimbo and Miwa using the quantum affine symmetry of the model, and of their adaptation to the isotropic case by Abada, Bougourzi and Si-Lakhal (correcting some overall factors). The 4-spinon contribution to the first frequency moment sum rule at fixed momentum is calculated. This shows, as expected, that most of the remaining correlation weight above the known 2-spinon part is carried by 4-spinon states. Our results therefore provide an extremely accurate description of the exact structure factor.Comment: 13 page

Modelling the 3D physical structure of astrophysical sources with GASS

The era of interferometric observations leads to the need of a more and more precise description of physical structures and dynamics of star-forming regions, from pre-stellar cores to protoplanetary discs. The molecular emission can be traced in multiple physical components such as infalling envelopes, outflows and protoplanetary discs. To compare with the observations, a precise and complex radiative transfer modelling of these regions is needed. We present GASS (Generator of Astrophysical Sources Structure), a code that allows us to generate the three-dimensional (3D) physical structure model of astrophysical sources. From the GASS graphical interface, the user easily creates different components such as spherical envelopes, outflows and discs. The physical properties of these components are modelled thanks to dedicated graphical interfaces that display various figures in order to help the user and facilitate the modelling task. For each component, the code randomly generates points in a 3D grid with a sample probability weighted by the molecular density. The created models can be used as the physical structure input for 3D radiative transfer codes to predict the molecular line or continuum emission. An analysis of the output hyper-spectral cube given by such radiative transfer code can be made directly in GASS using the various post-treatment options implemented, such as calculation of moments or convolution with a beam. This makes GASS well suited to model and analyse both interferometric and single-dish data. This paper is focused on the results given by the association of GASS and LIME, a 3D radiative transfer code, and we show that the complex geometry observed in star-forming regions can be adequately handled by GASS+LIME

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

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 $S^{+-}(k,\omega)$. 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\cdot$2N(C$_5$D$_5$).Comment: 4 pages, 1 figure, 1 tabl

Split Fermi seas in one-dimensional Bose fluids

For the one-dimensional repulsive Bose gas (Lieb-Liniger model), we study a special class of highly-excited states obtained by giving a finite momentum to subgroups of particles. These states, which correspond to `splitting' the ground state Fermi sea-like quantum number configuration, are zero-entropy states which display interesting properties more normally associated to ground states. Using a numerically exact method based on integrability, we study these states' excitation spectrum, density correlations and momentum distribution functions. These correlations display power-law asymptotics, and are shown to be accurately described by an effective multicomponent Tomonaga-Luttinger liquid theory whose parameters are obtained from Bethe Ansatz. The non-universal correlation prefactors are moreover obtained from integrability, yielding a completely parameter-free fit of the correlator asymptotics.Comment: 10 pages, 14 figure

Spatially Anisotropic Heisenberg Kagome Antiferromagnet

We study the quasi-one-dimensional limit of the spin-1/2 quantum Heisenberg antiferromagnet on the kagome lattice. The lattice is divided into antiferromagnetic spin-chains (exchange J) that are weakly coupled via intermediate "dangling" spins (exchange J'). Using one-dimensional bosonization, renormalization group methods, and current algebra techniques the ground state is determined in the limit J'<<J. We find that the dangling spins and chain spins form a spiral with O(1) and O(J'/J) static moments, respectively, atop of which the chain spins exhibit a smaller O[(J'/J)^2] antiferromagnetically ordered component along the axis perpendicular to the spiral plane.Comment: 17 pages, 3 figures, corrected sign error, corrected typos, updated reference

Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases

Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models possess non-trivial conserved quantities beyond energy and momentum. These quantities are believed to control dynamics and thermalization in low dimensional atomic gases as well as in quantum spin chains. But what happens when the special symmetries leading to the existence of the extra conserved quantities are broken? Is there any memory of the quantities if the breaking is weak? Here, in the presence of weak integrability breaking, we show that it is possible to construct residual quasi-conserved quantities, so providing a quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We demonstrate this construction explicitly in the context of quantum quenches in one-dimensional Bose gases and argue that these quasi-conserved quantities can be probed experimentally.Comment: 21 pages with appendices; 13 figures; version accepted by PR

Dynamical density-density correlations in the one-dimensional Bose gas

The zero-temperature dynamical structure factor of the one-dimensional Bose gas with delta-function interaction (Lieb-Liniger model) is computed using a hybrid theoretical/numerical method based on the exact Bethe Ansatz solution, which allows to interpolate continuously between the weakly-coupled Thomas-Fermi and strongly-coupled Tonks-Girardeau regimes. The results should be experimentally accessible with Bragg spectroscopy.Comment: 4 pages, 3 figures, published versio

Electron Interactions and Transport Between Coupled Quantum Hall Edges

We examine the effects of electron-electron interactions on transport between edge states in a multilayer integer quantum Hall system. The edge states of such a system, coupled by interlayer tunneling, form a two-dimensional, chiral metal at the sample surface. We calculate the temperature-dependent conductivity and the amplitude of conductance fluctuations in this chiral metal, treating Coulomb interactions and disorder exactly in the weak-tunneling limit. We find that the conductivity increases with increasing temperature, as observed in recent experiments, and we show that the correlation length characterising conductance fluctuations varies inversely with temperature.Comment: 4 pages, 2 figures, typos corrected, Ref. 17 added, minor changes made for publicatio

Impact of the annealing temperature on Pt/g-C3N4 structure, activity and selectivity between photodegradation and water splitting

Acknowledgements: The authors would like to thank SABIC as well as EPSRC platform grant [EP/K015540/1] for financial support and the Royal Society of Chemistry for a Wolfson Merit Award. In order to protect intellectual property the data underpinning this publication are not made publicly available. All enquiries about the data should be addressed to [email protected] reviewedPostprin