Adiabatic Continuation of Fractional Chern Insulators to Fractional Quantum Hall States

We show how the phases of interacting particles in topological flat bands, known as fractional Chern insulators, can be adiabatically connected to incompressible fractional quantum Hall liquids in the lowest Landau-level of an externally applied magnetic field. Unlike previous evidence suggesting the similarity of these systems, our approach enables a formal proof of the equality of their topological orders, and furthermore this proof robustly extends to the thermodynamic limit. We achieve this result using the hybrid Wannier orbital basis proposed by Qi [Phys. Rev. Lett. 107, 126803 (2011)] in order to construct interpolation Hamiltonians that provide continuous deformations between the two models. We illustrate the validity of our approach for the groundstate of bosons in the half filled Chern band of the Haldane model, showing that it is adiabatically connected to the nu=1/2 Laughlin state of bosons in the continuum fractional quantum Hall problem

Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number.

The Harper-Hofstadter model provides a fractal spectrum containing topological bands of any integer Chern number C. We study the many-body physics that is realized by interacting particles occupying Harper-Hofstadter bands with |C|>1. We formulate the predictions of Chern-Simons or composite fermion theory in terms of the filling factor ν, defined as the ratio of particle density to the number of single-particle states per unit area. We show that this theory predicts a series of fractional quantum Hall states with filling factors ν=r/(r|C|+1) for bosons, or ν=r/(2r|C|+1) for fermions. This series includes a bosonic integer quantum Hall state in |C|=2 bands. We construct specific cases where a single band of the Harper-Hofstadter model is occupied. For these cases, we provide numerical evidence that several states in this series are realized as incompressible quantum liquids for bosons with contact interactions.The authors acknowledge support from the Leverhulme Trust under Grant No. ECF-2011-565, from the Isaac Newton Trust, and by the Royal Society under Grant No. UF120157 (G. M.), as well as by Engineering and Physical Sciences Research Council Grants No. EP/J017639/1 and No. EP/K030094/1 (N. R. C.).This is the author accepted manuscript. The final version is available from APS via http://dx.doi.org/10.1103/PhysRevLett.115.12640

Geometric stability of topological lattice phases.

The fractional quantum Hall (FQH) effect illustrates the range of novel phenomena which can arise in a topologically ordered state in the presence of strong interactions. The possibility of realizing FQH-like phases in models with strong lattice effects has attracted intense interest as a more experimentally accessible venue for FQH phenomena which calls for more theoretical attention. Here we investigate the physical relevance of previously derived geometric conditions which quantify deviations from the Landau level physics of the FQHE. We conduct extensive numerical many-body simulations on several lattice models, obtaining new theoretical results in the process, and find remarkable correlation between these conditions and the many-body gap. These results indicate which physical factors are most relevant for the stability of FQH-like phases, a paradigm we refer to as the geometric stability hypothesis, and provide easily implementable guidelines for obtaining robust FQH-like phases in numerical or real-world experiments.R. R. acknowledges support from the Sloan Foundation. G. M. acknowledges support from the Leverhulme Trust under grant no. ECF-2011-565, from the Newton Trust of the University of Cambridge, and from the Royal Society under grant UF120157. This work used computational and storage services associated with the Hoffman2 Shared Cluster provided by UCLA Institute for Digital Research and Education’s Research Technology Group. Part of our numerical work was performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service funded by Strategic Research Infrastructure Funding from the Higher Education Funding Council for England and funding from the Science and Technology Facilities Council.This is the final version of the article. It first appeared from Nature Publishing Group via http://dx.doi.org/10.1038/ncomms962

Paired composite fermion phase of quantum Hall bilayers at \nu = 1/2 + 1/2

We provide numerical evidence for composite fermion pairing in quantum Hall bilayer systems at filling $\nu=1/2 + 1/2$ for intermediate spacing between the layers. We identify the phase as $p_x + i p_y$ pairing, and construct high accuracy trial wavefunctions to describe the groundstate on the sphere. For large distances between the layers, and for finite systems, a competing "Hund's rule" state, or composite fermion liquid, prevails for certain system sizes. We argue that for larger systems, the pairing phase will persist to larger layer spacing.Comment: 4 pages, 2 figures; v2: final version, as published in journa

Coaggregation of FcεRI with FcγRIIB Inhibits Degranulation but Not Induction of Bcl-2 Family Members A1 and Bim in Mast Cells

<p/> <p>The aggregation of high-affinity immunoglobulin E (IgE) receptors (FcεRI) on mast cells is a critical event in the initiation of an allergic reaction. Coengagement of FcεRI with immunoglobulin G (IgG) low-affinity receptor FcγRIIB/CD32 inhibits degranulation and the release of inflammatory mediators from mast cells and has therefore been proposed as a new therapeutic approach for the treatment of allergies. In this study, we investigated whether FcγRIIB, besides inhibiting degranulation, negatively regulates other signalling pathways downstream of FcεRI. For this, we determined the phosphorylation and/or expression of proteins involved in the regulation of mast-cell apoptosis. Coaggregation led to an attenuation of Akt phosphorylation but did not inhibit phosphorylation of transcription factor Foxo3a or its proapoptotic target, Bim. Similarly, FcεRI-dependent expression of the prosurvival gene A1 was not affected by coaggregation. Our data demonstrate that coengagement of FcεRI and FcγRIIB inhibits degranulation but not the signalling pathways regulating Bcl-2 family members Bim and A1.</p

Artificial Square Ice and Related Dipolar Nanoarrays

We study a frustrated dipolar array recently manufactured lithographically by Wang et al. [Nature (London) 439, 303 (2006)] in order to realize the square ice model in an artificial structure. We discuss models for thermodynamics and dynamics of this system. We show that an ice regime can be stabilized by small changes in the array geometry; a different magnetic state, kagome ice, can similarly be constructed. At low temperatures, the square ice regime is terminated by a thermodynamic ordering transition, which can be chosen to be ferro- or antiferromagnetic. We show that the arrays do not fully equilibrate experimentally, and identify a likely dynamical bottleneck

Numerical Evidence for a p_x - ip_y Paired Fractional Quantum Hall State at ν = 12/5

We provide numerical evidence supporting a Bonderson–Slingerland (BS) non-Abelian hierarchy state as a candidate for the observed ν = 12/5 quantum Hall plateau. We confirm the existence of a gapped incompressible ν = 12/5 quantum Hall state with shift S = 2 matching that of the BS state. The exact ground-state of the Coulomb interaction state on the sphere is shown to have large overlap with the BS ground-state trial wavefunction. The analysis of the BS states is extended to hierarchical descendants of general paired states in the weak-pairing phase at ν = 5/2

Composite Fermions in Negative Effective Magnetic Field: A Monte-Carlo Study

The method of Jain and Kamilla [PRB {\bf 55}, R4895 (1997)] allows numerical generation of composite fermion trial wavefunctions for large numbers of electrons in high magnetic fields at filling fractions of the form nu=p/(2mp+1) with m and p positive integers. In the current paper we generalize this method to the case where the composite fermions are in an effective (mean) field with opposite sign from the actual physical field, i.e. when p is negative. We examine both the ground state energies and the low energy neutral excitation spectra of these states. Using particle-hole symmetry we can confirm the correctness of our method by comparing results for the series m=1 with p>0 (previously calculated by others) to our results for the conjugate series m=1 with p <0. Finally, we present similar results for ground state energies and low energy neutral excitations for the states with m=2 and p <0 which were not previously addressable, comparing our results to the m=1 case and the p > 0, m=2 cases.Comment: 11 page

Synthetic Gauge Fields for Lattices with Multi-Orbital Unit Cells: Routes towards a π\pi-flux Dice Lattice with Flat Bands

We propose a general strategy for generating synthetic magnetic fields in complex lattices with non-trivial connectivity based on light-matter coupling in cold atomic gases. Our approach starts from an underlying optical flux lattice in which a synthetic magnetic field is generated by coupling several internal states. Starting from a high symmetry optical flux lattice, we superpose a scalar potential with a super- or sublattice period in order to eliminate links between the original lattice sites. As an alternative to changing connectivity, the approach can also be used to create or remove lattice sites from the underlying parent lattice. To demonstrate our concept, we consider the dice lattice geometry as an explicit example, and construct a dice lattice with a flux density of half a flux quantum per plaquette, providing a pathway to flat bands with a large band gap. While the intuition for our proposal stems from the analysis of deep optical lattices, we demonstrate that the approach is robust even for shallow optical flux lattices far from the tight-binding limit. We also provide an alternative experimental proposal to realise a synthetic gauge field in a fully frustrated dice lattice based on laser-induced hoppings along individual bonds of the lattice, again involving a superlattice potential. In this approach, atoms with a long-lived excited state are trapped using an 'anti-magic' wavelength of light, allowing the desired complex hopping elements to be induced in a specific laser coupling scheme for the dice lattice geometry. We conclude by comparing the complexity of these alternative approaches, and advocate that complex optical flux lattices provide the more elegant and easily generalisable strategy