Detecting fractional Chern insulators through circular dichroism

Great efforts are currently devoted to the engineering of topological Bloch bands in ultracold atomic gases. Recent achievements in this direction, together with the possibility of tuning inter-particle interactions, suggest that strongly-correlated states reminiscent of fractional quantum Hall (FQH) liquids could soon be generated in these systems. In this experimental framework, where transport measurements are limited, identifying unambiguous signatures of FQH-type states constitutes a challenge on its own. Here, we demonstrate that the fractional nature of the quantized Hall conductance, a fundamental characteristic of FQH states, could be detected in ultracold gases through a circular-dichroic measurement, namely, by monitoring the energy absorbed by the atomic cloud upon a circular drive. We validate this approach by comparing the circular-dichroic signal to the many-body Chern number, and discuss how such measurements could be performed to distinguish FQH-type states from competing states. Our scheme offers a practical tool for the detection of topologically-ordered states in quantum-engineered systems, with potential applications in solid state.Comment: Revised versio

Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles

Realizing strongly-correlated topological phases of ultracold gases is a central goal for ongoing experiments. And while fractional quantum Hall states could soon be implemented in small atomic ensembles, detecting their signatures in few-particle settings remains a fundamental challenge. In this work, we numerically analyze the center-of-mass Hall drift of a small ensemble of hardcore bosons, initially prepared in the ground state of the Harper-Hofstadter-Hubbard model in a box potential. By monitoring the Hall drift upon release, for a wide range of magnetic flux values, we identify an emergent Hall plateau compatible with a fractional Chern insulator state: the extracted Hall conductivity approaches a fractional value determined by the many-body Chern number, while the width of the plateau agrees with the spectral and topological properties of the prepared ground state. Besides, a direct application of Streda's formula indicates that such Hall plateaus can also be directly obtained from static density-profile measurements. Our calculations suggest that fractional Chern insulators can be detected in cold-atom experiments, using available detection methods.Comment: 13 pages, 11 figures; extended version accepted for publicatio

Stability of the spin-1/21/2 kagome ground state with breathing anisotropy

We numerically study the spin-$1/2$ breathing kagome lattice. In this variation of the kagome Heisenberg antiferromagnet, the spins belonging to upward and downward facing triangles have different coupling strengths. Using the density matrix renormalization group (DMRG) method and exact diagonalization, we show that the kagome antiferromagnet spin liquid is extremely robust to this anisotropy. Materials featuring this anisotropy -- and especially the recently studied vanadium compound $[{\mathrm{NH}}_{4}{]}_{2}[{\mathbf{C}}_{7}{\mathbf{H}}_{14}\mathbf{N}][{\mathbf{V}}_{7}{\mathbf{O}}_{6}{\mathbf{F}}_{18}]$ (DQVOF) -- may thus be very good candidates to realize the much studied kagome spin liquid. Further, we closely examine the limit of strong breathing anisotropy and find indications of a transition to a nematic phase.Comment: 12 pages, 15 figure

Z2\mathbb Z_2 fractional topological insulators in two dimensions

We propose a simple microscopic model to numerically investigate the stability of a two dimensional fractional topological insulator (FTI). The simplest example of a FTI consists of two decoupled copies of a Laughlin state with opposite chiralities. We focus on bosons at half filling. We study the stability of the FTI phase upon addition of two coupling terms of different nature: an interspin interaction term, and an inversion symmetry breaking term that couples the copies at the single particle level. Using exact diagonalization and entanglement spectra, we numerically show that the FTI phase is stable against both perturbations. We compare our system to a similar bilayer fractional Chern insulator. We show evidence that the time reversal invariant system survives the introduction of interaction coupling on a larger scale than the time reversal symmetry breaking one, stressing the importance of time reversal symmetry in the FTI phase stability. We also discuss possible fractional phases beyond $\nu = 1/2$.Comment: 15 pages, 18 figure

Projective construction of the Zk\mathbb{Z}_k Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry

Multilayer fractional quantum Hall wave functions can be used to construct the non-Abelian states of the $\mathbb{Z}_k$ Read-Rezayi series upon symmetrization over the layer index. Unfortunately, this construction does not yield the complete set of $\mathbb{Z}_k$ ground states on the torus. We develop an alternative projective construction of $\mathbb{Z}_k$ Read-Rezayi states that complements the existing one. On the multi-layer torus geometry, our construction consists of introducing twisted boundary conditions connecting the layers before performing the symmetrization. We give a comprehensive account of this construction for bosonic states, and numerically show that the full ground state and quasihole manifolds are recovered for all computationally accessible system sizes. Furthermore, we analyze the neutral excitation modes above the Moore-Read on the torus through an extensive exact diagonalization study. We show numerically that our construction can be used to obtain excellent approximations to these modes. Finally, we extend the new symmetrization scheme to the plane and sphere geometries.Comment: 19 pages, 9 figure

Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures

Fractional quantum Hall-superconductor heterostructures may provide a platform towards non-abelian topological modes beyond Majoranas. However their quantitative theoretical study remains extremely challenging. We propose and implement a numerical setup for studying edge states of fractional quantum Hall droplets with a superconducting instability. The fully gapped edges carry a topological degree of freedom that can encode quantum information protected against local perturbations. We simulate such a system numerically using exact diagonalization by restricting the calculation to the quasihole-subspace of a (time-reversal symmetric) bilayer fractional quantum Hall system of Laughlin $\nu=1/3$ states. We show that the edge ground states are permuted by spin-dependent flux insertion and demonstrate their fractional $6\pi$ Josephson effect, evidencing their topological nature and the Cooper pairing of fractionalized quasiparticles.Comment: 12 pages, 9 figure

Triplet FFLO Superconductivity in the doped Kitaev-Heisenberg Honeycomb Model

We provide analytical and numerical evidence of a spin-triplet FFLO superconductivity in the itinerant Kitaev-Heisenberg model (anti-ferromagnetic Kitaev coupling and ferromagnetic Heisenberg coupling) on the honeycomb lattice around quarter filling. The strong spin-orbit coupling in our model leads to the emergence of 6 inversion symmetry centers for the Fermi surface at non zero momenta in the first Brillouin zone. We show how the Cooper pairs condense into these non-trivial momenta, causing the spatial modulation of the superconducting order parameter. Applying a Ginzburg-Landau expansion analysis, we find that the superconductivity has three separated degenerate ground states with three different spin-triplet pairings. This picture is also supported by exact diagonalizations on finite clusters

Evaluation of heat treated wood swelling by differential scanning calorimetry in relation with chemical composition

24 pagesInternational audienceRetification® is a heat treatment which decreases the swelling of wood and increases its resistance to fungal attack. In this study, differential scanning calorimetry (DSC) was applied in order to determine the fiber saturation point (FSP) of natural and retified® wood. FSP values were used to determine the total swelling of natural and heat-treated wood. The DSC method was compared to the volumetric shrinkage approach. The influence of the heat treatment temperature and duration on the swelling of wood was investigated. Relationships between chemical changes and the reduction of swelling were analysed thoroughly. The equivalence of the DSC method and the volumetric shrinkage method is shown. FSP in association with anhydrous density is a good indicator for the evaluation of the overall swelling of heat-treated wood. Reduction of wood swelling with increasing temperature and duration of thermal treatment is often attributed to hemicelluloses destruction. This study shows that the reduction of beech wood swelling can not only be attributed to the disappearing of adsorption sites that goes with the hemicelluloses destruction. It is suggested that other phenomena such as structural modifications and chemical changes of lignin also play an important part

Evaluation of heat treated beech by non destructive testing

10 pagesImprovement of dimensional stability and durability is wished for the use of wood as a building material. For the last decade, retification® has been industrially developed. It consists in a stabilization and preservation of wood by heat treatment. The aim of this study is to find simple and fast methods to characterize heat treated beech. Non destructive testing is expected to be relevant to evaluate the level of treatment and the properties for the use of heat treated wood. Six treatments were carried out in a pilot reactor. The parameters of the retification® stage (temperature and time) were studied. For each treatment, the non destructive tests (free oscillations in the fundamental mode, colour and dry weight loss)were performed, and the properties for use (mechanical resistance and volumetric shrinkage) measured. Lightness and dry weight loss seem to be suitable properties to characterize beech retification® when the time parameter is fixed. However, they are not suitable for other wood species, and for retification stages with a variable duration. Moreover, the correlation with the properties for use were plotted, but presented too large dispersion to be relevant. After correction of moisture content, the longitudinal Young's modulus of the material is slightly increased by each of the six treatments, but do not present any variation with changing parameters values. On the contrary, the mechanical resistance decreased with increasing temperature and time. Thus the dynamic Young's modulus is not reliable to evaluate the treatment and to predict the loss of mechanical resistance. The logarithmic decrement was not increased by any of the treatments, which is in opposition with the hypothesis that retification® generates cracks and microcracks in the material. Effects of long time at low temperature have been investigated. From these experiments, properties of treated wood may be improved significantly by choosing appropriate values of the parameters