The Fractional Quantum Hall States at ν=13/5\nu=13/5 and 12/512/5 and their Non-Abelian Nature

We investigate the nature of the fractional quantum Hall (FQH) state at filling factor $\nu=13/5$, and its particle-hole conjugate state at $12/5$, with the Coulomb interaction, and address the issue of possible competing states. Based on a large-scale density-matrix renormalization group (DMRG) calculation in spherical geometry, we present evidence that the physics of the Coulomb ground state (GS) at $\nu=13/5$ and $12/5$ is captured by the $k=3$ parafermion Read-Rezayi RR state, $\text{RR}_3$. We first establish that the state at $\nu=13/5$ is an incompressible FQH state, with a GS protected by a finite excitation gap, with the shift in accordance with the RR state. Then, by performing a finite-size scaling analysis of the GS energies for $\nu=12/5$ with different shifts, we find that the $\text{RR}_3$ state has the lowest energy among different competing states in the thermodynamic limit. We find the fingerprint of $\text{RR}_3$ topological order in the FQH $13/5$ and $12/5$ states, based on their entanglement spectrum and topological entanglement entropy, both of which strongly support their identification with the $\text{RR}_3$ state. Furthermore, by considering the shift-free infinite-cylinder geometry, we expose two topologically-distinct GS sectors, one identity sector and a second one matching the non-Abelian sector of the Fibonacci anyonic quasiparticle, which serves as additional evidence for the $\text{RR}_3$ state at $13/5$ and $12/5$.Comment: 12 pages, 8 figure

Topology of Charge Density from Pseudopotential Density Functional Theory Calculations

The absence of core electrons in pseudopotential electronic structure calculations poses some important problems on determining the topology of density. The key feature of valence-only densities is the lack of critical points (CPs) at the nuclear positions affected by core removal, which are sometimes substituted by local minimum CPs, the substitution of a maximum by a minimum must be necessarily accompanied by the creation of other compensating CPs, including at least either one maximum or one ring CP. As density is relatively unaffected at distance points far enough the removed cores, these new CPs are expected to lie in the proximity of the latter, and the topology of density to closely resemble that of the AE density in the chemically relevant valence regions. This difficulty is well-known in literature, and several works have been devoted to elucidate how to bypass it (Cioslowski and Piskorz, 1996). The correct topologies may be obtained from core-reconstructed pseudo-AE densities. This paper will show how the correct topology can be obtained from pseudopotential calculations. In order to analyze the problems that arise from the core electrons, results obtained for Alanine (CH3CH (NH2) COOH), Aminophenol (C6H4 (OH) NH2), Ethene (C2H4), and Propanone ((CH3)2CO) using all-electron, pseudo-valence wavefunctions are reported. Keywords: Pseudopotential, core electrons, all-electron (AE) density, QTAIM, charge density topology

Density functional simulation of small Fe nanoparticles

We calculate from first principles the electronic structure, relaxation and magnetic moments in small Fe particles, applying the numerical local orbitals method in combination with norm-conserving pseudopotentials. The accuracy of the method in describing elastic properties and magnetic phase diagrams is tested by comparing benchmark results for different phases of crystalline iron to those obtained by an all-electron method. Our calculations for the bipyramidal Fe_5 cluster qualitatively and quantitatively confirm previous plane-wave results that predicted a non-collinear magnetic structure. For larger bcc-related (Fe_35) and fcc-related (Fe_38, Fe_43, Fe_62) particles, a larger inward relaxation of outer shells has been found in all cases, accompanied by an increase of local magnetic moments on the surface to beyond 3 mu_B.Comment: 15 pages with 6 embedded postscript figures, updated version, submitted to Eur.Phys.J.

Surface States of the Topological Insulator Bi_{1-x}Sb_x

We study the electronic surface states of the semiconducting alloy BiSb. Using a phenomenological tight binding model we show that the Fermi surface of the 111 surface states encloses an odd number of time reversal invariant momenta (TRIM) in the surface Brillouin zone confirming that the alloy is a strong topological insulator. We then develop general arguments which show that spatial symmetries lead to additional topological structure, and further constrain the surface band structure. Inversion symmetric crystals have 8 Z_2 "parity invariants", which include the 4 Z_2 invariants due to time reversal. The extra invariants determine the "surface fermion parity", which specifies which surface TRIM are enclosed by an odd number of electron or hole pockets. We provide a simple proof of this result, which provides a direct link between the surface states and the bulk parity eigenvalues. We then make specific predictions for the surface state structure for several faces of BiSb. We next show that mirror invariant band structures are characterized by an integer "mirror Chern number", n_M. The sign of n_M in the topological insulator phase of BiSb is related to a previously unexplored Z_2 parameter in the L point k.p theory of pure Bi, which we refer to as the "mirror chirality", \eta. The value of \eta predicted by the tight binding model for Bi disagrees with the value predicted by a more fundamental pseudopotential calculation. This explains a subtle disagreement between our tight binding surface state calculation and previous first principles calculations on Bi. This suggests that the tight binding parameters in the Liu Allen model of Bi need to be reconsidered. Implications for existing and future ARPES experiments and spin polarized ARPES experiments will be discussed.Comment: 15 pages, 7 figure

The wavefunction reconstruction effects in calculation of DM-induced electronic transition in semiconductor targets

The physics of the electronic excitation in semiconductors induced by sub-GeV dark matter (DM) have been extensively discussed in literature, under the framework of the standard plane wave (PW) and pseudopotential calculation scheme. In this paper, we investigate the implication of the all-electron (AE) reconstruction on estimation of the DM-induced electronic transition event rates. As a benchmark study, we first calculate the wavefunctions in silicon and germanium bulk crystals based on both the AE and pseudo (PS) schemes within the projector augmented wave (PAW) framework, and then make comparisons between the calculated excitation event rates obtained from these two approaches. It turns out that in process where large momentum transfer is kinetically allowed, the two calculated event rates can differ by a factor of a few. Such discrepancies are found to stem from the high-momentum components neglected in the PS scheme. It is thus implied that the correction from the AE wavefunction in the core region is necessary for an accurate estimate of the DM-induced transition event rate in semiconductors.Comment: A missing factor $64^{-3/2}=1/512$ associated with the Fourier transformation is added to both the AE and PS event rates in this version. The ratio between the AE and PS event rates is not affecte

Electronic correlation in the quantum Hall regime

Two-dimensional interacting electron systems become strongly correlated if the electrons are subject to a perpendicular high magnetic field. After introducing the physics of the quantum Hall regime the incompressible many- particle ground state and its excitations are studied in detail at fractional filling factors for spin-polarized electrons. The spin degree of freedom whose importance was shown in recent experiments is considered by studying the thermodynamics at filling factor one and near one.Comment: 55 pages, 26 eps-figure

Development and application of statistical and quantum mechanical methods for modelling molecular ensembles

The development of new quantum chemical methods requires extensive benchmarking to establish the accuracy and limitations of a method. Current benchmarking practices in computational chemistry use test sets that are subject to human biases and as such can be fundamentally flawed. This work presents a thorough benchmark of diffusion Monte Carlo (DMC) for a range of systems and properties as well as a novel method for developing new, unbiased test sets using multivariate statistical techniques. Firstly, the hydrogen abstraction of methanol is used as a test system to develop a more efficient protocol that minimises the computational cost of DMC without compromising accuracy. This protocol is then applied to three test sets of reaction energies, including 43 radical stabilisation energies, 14 Diels-Alder reactions and 76 barrier heights of hydrogen and non-hydrogen transfer reactions. The average mean absolute error for all three databases is just 0.9 kcal/mol. The accuracy of the explicitly correlated trial wavefunction used in DMC is demonstrated using the ionisation potentials and electron affinities of first- and second-row atoms. A multi-determinant trial wavefunction reduces the errors for systems with strong multi-configuration character, as well as for predominantly single-reference systems. It is shown that the use of pseudopotentials in place of all-electron basis sets slightly increases the error for these systems. DMC is then tested with a set of eighteen challenging reactions. Incorporating more determinants in the trial wavefunction reduced the errors for most systems but results are highly dependent on the active space used in the CISD wavefunction. The accuracy of multi-determinant DMC for strongly multi-reference systems is tested for the isomerisation of diazene. In this case no method was capable of reducing the error of the strongly-correlated rotational transition state. Finally, an improved method for selecting test sets is presented using multivariate statistical techniques. Bias-free test sets are constructed by selecting archetypes and prototypes based on numerical representations of molecules. Descriptors based on the one-, two- and three-dimensional structures of a molecule are tested. These new test sets are then used to benchmark a number of methods

Topological Flat Band Models and Fractional Chern Insulators

Topological insulators and their intriguing edge states can be understood in a single-particle picture and can as such be exhaustively classified. Interactions significantly complicate this picture and can lead to entirely new insulating phases, with an altogether much richer and less explored phenomenology. Most saliently, lattice generalizations of fractional quantum Hall states, dubbed fractional Chern insulators, have recently been predicted to be stabilized by interactions within nearly dispersionless bands with non-zero Chern number, $C$. Contrary to their continuum analogues, these states do not require an external magnetic field and may potentially persist even at room temperature, which make these systems very attractive for possible applications such as topological quantum computation. This review recapitulates the basics of tight-binding models hosting nearly flat bands with non-trivial topology, $C\neq 0$, and summarizes the present understanding of interactions and strongly correlated phases within these bands. Emphasis is made on microscopic models, highlighting the analogy with continuum Landau level physics, as well as qualitatively new, lattice specific, aspects including Berry curvature fluctuations, competing instabilities as well as novel collective states of matter emerging in bands with $|C|>1$. Possible experimental realizations, including oxide interfaces and cold atom implementations as well as generalizations to flat bands characterized by other topological invariants are also discussed.Comment: Invited review. 46 pages, many illustrations and references. V2: final version with minor improvements and added reference