Wavefunctions for topological quantum registers

We present explicit wavefunctions for quasi-hole excitations over a variety of non-abelian quantum Hall states: the Read-Rezayi states with k ? 3 clustering properties and a paired spin-singlet quantum Hall state. Quasi-holes over these states constitute a topological quantum register, which can be addressed by braiding quasi-holes. We obtain the braid properties by direct inspection of the quasi-hole wavefunctions. We establish that the braid properties for the paired spin-singlet state are those of ‘Fibonacci anyons’, and thus suitable for universal quantum computation. Our derivations in this paper rely on explicit computations in the parafermionic conformal field theories that underly these particular quantum Hall states.     

Quantum Hall effect in higher dimensions

Following recent work on the quantum Hall effect on S⁴, we solve the Landau problem on the complex projective spaces $\text{C}\text{P}{}^{\mathrm{k}}$ and discuss quantum Hall states for such spaces. Unlike the case of S⁴, a finite spatial density can be obtained with a finite number of internal states for each particle. We treat the case of $\text{C}\text{P}{}^2$ in some detail considering both Abelian and nonAbelian background fields. The wavefunctions are obtained and incompressibility of the Hall states is shown. The case of $\text{C}\text{P}{}^3$ is related to the case of S⁴.     

Yang-Baxter algebras of monodromy matrices in integrable quantum field theories

We consider a large class of two-dimensional integrable quantum field theories with non-abelian internal symmetry and classical scale invariance. We present a general procedure to determine explicitly the conserved quantum monodromy operator generating infinitely many non-local charges. The main features of our method are a factorization principle and the use of $\text{P}$, $\text{T}$, and internal symmetries. The monodromy operator is shown to satisfy a Yang-Baxter algebra, the structure constants (i.e. the quantum R-matrix) of which are determined by two-particle S-matrix of the theory. We apply the method to the chiral SU(N) and the O(2N) Gross-Neveu models.     

Landau-Ginzburg theories for non-abelian quantum Hall states

We construct Landau-Ginzburg effective field theories for fractional quantum Hall states - such as the Pfaffian state - which exhibit non-abelian statistics. These theories rely on a Meissner construction which increases the level of a non-abelian Chem-Simons theory while simultaneously projecting out the unwanted degrees of freedom of a concomitant enveloping abelian theory. We describe this construction in the context of a system of bosons at Landau level filling factor ν = l, where the non-abelian symmetry is a dynamically generated SU(2) continuous extension of the discrete particle-hole symmetry of the lowest Landau level. We show how the physics of quasiparticles and their non-abelian statistics arises in this Landau-Ginzburg theory. We describe its relation to edge theories - where a coset construction plays the role of the Meissner projection — and discuss extensions to other states.     

Non-abelian exclusion statistics

We introduce the notion of ‘order-k non-abelian exclusion statistics’. We derive the associated thermodynamic equations by employing the thermodynamic Bethe ansatz for specific non-diagonal scattering matrices. We make contact with results obtained by different methods and we point out connections with ‘fermionic sum formulas’ for characters in a conformal field theory. As an application, we derive thermodynamic distribution functions for quasi-holes over a class of non-abelian quantum Hall states recently proposed by Read and Rezayi.     

Non-abelian spin-singlet quantum Hall states: wave functions and quasihole state counting

We investigate a class of non-abelian spin-singlet (NASS) quantum Hall phases, proposed previously. The trial ground and quasihole excited states are exact eigenstates of certain (k+1)-body interaction Hamiltonians. The k=1 cases are the familiar Halperin abelian spin-singlet states. We present closed-form expressions for the many-body wave functions of the ground states, which for k>1 were previously defined only in terms of correlators in specific conformal field theories. The states contain clusters of k electrons, each cluster having either all spins up, or all spins down. The ground states are non-degenerate, while the quasihole excitations over these states show characteristic degeneracies, which give rise to non-abelian braid statistics. Using conformal field theory methods, we derive counting rules that determine the degeneracies in a spherical geometry. The results are checked against explicit numerical diagonalization studies for small numbers of particles on the sphere.     

A plasma analogy and Berry matrices for non-abelian quantum Hall states

We present an approach to the computation of the non-abelian statistics of quasiholes in quantum Hall states, such as the Pfaffian state, whose wavefunctions are related to the conformal blocks of minimal model conformal field theories. We use the Coulomb gas construction of these conformal field theories to formulate a plasma analogy for the quantum Hall states. A number of properties of the Pfaffian state follow immediately, including the Berry phases, which demonstrate the quasiholes' fractional charge, the abelian statistics of the two-quasihole state, and equal-time ground state correlation functions. The non-abelian statistics of multi-quasihole states follows from an additional assumption.     

Electron and quasiparticle exponents of Haldane-Rezayi state in non-abelian fractional quantum Hall theory

The quasiparticle propagator of the Haldane-Rezayi (HR) fractional quantum Hall (FQH) state is calculated, based on a chiral fermion model (or a Weyl fermion model) equipped with a hidden spin SU(2) symmetry. The spectrum of the chiral fermion model for each total spin and total momentum is shown to be identical to that of the SU(2) c = −2 model introduced to describe the edge spectrum of the HR state.     

The Haldane-Rezayi quantum Hall state and conformal field theory

We propose field theories for the bulk and edge of a quantum Hall state in the universality class of the Haldane-Rezayi wavefunction. The bulk theory is associated with the c = −2 conformal field theory. The topological properties of the state, such as the quasiparticle braiding statistics and ground state degeneracy on a torus, may be deduced from this conformal field theory. The 10-fold degeneracy on a torus is explained by the existence of a logarithmic operator in the c = −2 theory; this operator corresponds to a novel bulk excitation in the quantum Hall state. We argue that the edge theory is the c = 1 chiral Dirac fermion, which is related in a simple way to the c = −2 theory of the bulk. This theory is reformulated as a truncated version of a doublet of Dirac fermions in which the SU(2) symmetry - which corresponds to the spin-rotational symmetry of the quantum Hall system - is manifest and non-local. We make predictions for the current-voltage characteristics for transport through point contacts.     

Topological invariants for fractional quantum hall states

We calculate a topological invariant, whose value would coincide with the Chern number in the case of integer quantum Hall effect, for fractional quantum Hall states. In the case of Abelian fractional quantum Hall states, this invariant is shown to be equal to the trace of the K-matrix. In the case of non-Abelian fractional quantum Hall states, this invariant can be calculated on a case by case basis from the conformal field theory describing these states. This invariant can be used, for example, to distinguish between different fractional Hall states numerically even though, as a single number, it cannot uniquely label distinct states.     

Shallow acceptor bound exciton and free exciton states in high-purity zinc telluride

We investigated excitons bound to shallow acceptors in high-purity ZnTe and measured excitation spectra of two-hole luminescence lines at 1.6 K using a tunable dye-laser. The electron-hole coupling in the bound exciton (BE) states appears to be very different for the various acceptors even for almost identical exciton localisation energies. Three different types of BE are reported. For the Li-acceptor BE we observe three sub-components separated by 0.22 and 0.17 meV and interpreted as J = $\text{1}\text{2}$, $\text{3}\text{2}$, $\text{5}\text{2}$ states. The Ag-acceptor BE exhibits a strong ground state and a weak excited state at 1.3 meV higher energy. For the as yet unidentified k-acceptor we observe a single BE level, degenerate with the Ag-acceptor BE ground state. Dips in the excitation spectra due to absorption into free exciton 1S, 2S, and 3S states yield an exciton Rydberg R₀ = 12.8±0.3 meV and a free exciton binding energy FE(1S) = 13.2±0.3 meV.     

Non-abelian quantum Hall effect in topological flat bands

Inspired by the recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-abelian quantum Hall effect in lattice models with topological flat bands. Through extensive numerical studies on the Haldane model with three-body hard-core bosons loaded into a topological flat band, we find convincing numerical evidence of a stable ν=1 bosonic non-abelian quantum Hall effect, with the characteristic threefold quasidegeneracy of ground states on a torus, a quantized Chern number, and a robust spectrum gap. Moreover, the spectrum for two-quasihole states also shows a finite energy gap, with the number of states in the lower-energy sector satisfying the same counting rule as the Moore-Read pfaffian state.     

TFT construction of RCFT correlators I: partition functions

We formulate rational conformal field theory in terms of a symmetric special Frobenius algebra A and its representations. A is an algebra in the modular tensor category of Moore–Seiberg data of the underlying chiral CFT. The multiplication on A corresponds to the OPE of boundary fields for a single boundary condition. General boundary conditions are A-modules, and (generalised) defect lines are A–A-bimodules.The relation with three-dimensional TFT is used to express CFT data, like structure constants or torus and annulus coefficients, as invariants of links in three-manifolds. We compute explicitly the ordinary and twisted partition functions on the torus and the annulus partition functions. We prove that they satisfy consistency conditions, like modular invariance and NIM-rep properties.We suggest that our results can be interpreted in terms of non-commutative geometry over the modular tensor category of Moore–Seiberg data.     

Electron escape effects in photoemission from Ag(001) surfaces

We have observed electron escape effects, separate from excitation probabilities, in photoemission from clean Ag(001) surfaces. By comparison of angle-resolved photoemission data for the (001) surface of silver at several photon energies with a direct transition model based on calculated band structures, we have determined the dispersion $\text{E}\text{(}\text{k}{}_{\mathrm{\perp }}\text{+}\text{k}{}_{\mathrm{\parallel }}\text{)}$ of final states involved in the photoemiss ion process. Observed photoelectrons from Ag(001) are emitted into a single final state band, closely parallelled by the $\text{G}{}_{\mathrm{\parallel }}\text{= 0}$ branch of the nearly-free-electron fcc band structure, even though other final states $\text{(}\text{G}{}_{\mathrm{\parallel }}\text{≠0)}$ are dipole-allowed. This is interpreted as the preferentially strong overlap of only one allowed final state band with states external to the crystal.     

Anisotropic k-ƒ interactions from spin-orbit coupled 5d intermediate states

The anisotropy of the conduction electron-4? local moment interaction ($\text{k-?}$) gives rise to anisotropic transport effects. The contribution from the orbital character of the 4? moment has been well documented by magnetotransport studies on noble metals containing non-S state rare-earth ions. To determine whether there is an additional contribution to the anisotropy from the spin-orbit coupled 5d electron states we have studied the magnetoresistivity of Ag: Gd alloys. We have not found any significant anisotropy of the magnetoresistivity. By comparing this result and previous Hall effect and magnetoresistivity data on noble metal-rare earth alloys with our model calculation, we come to the conclusion that the spin-orbit splitting of the 5d virtual bound state is relatively small. We discuss the details of the resulting anisotropy of the $\text{k-?}$ interaction.     

Topological Entanglement Entropy from the Holographic Partition Function

We study the entropy of chiral 2+01-dimensional topological phases, where there are both gapped bulk excitations and gapless edge modes. We show how the entanglement entropy of both types of excitations can be encoded in a single partition function. This partition function is holographic because it can be expressed entirely in terms of the conformal field theory describing the edge modes. We give a general expression for the holographic partition function, and discuss several examples in depth, including abelian and non-abelian fractional quantum Hall states, and $p+ip$ superconductors. We extend these results to include a point contact allowing tunneling between two points on the edge, which causes thermodynamic entropy associated with the point contact to be lost with decreasing temperature. Such a perturbation effectively breaks the system in two, and we can identify the thermodynamic entropy loss with the loss of the edge entanglement entropy. From these results, we obtain a simple interpretation of the non-integer ‘ground state degeneracy’ which is obtained in 1+1-dimensional quantum impurity problems: its logarithm is a 2+1-dimensional topological entanglement entropy.     

The interaction of nucleons with antinucleons. III. Photon and pion emission from bound states

We calculate widths and branching ratios for the emission of γ rays or pions from a bound state of the nucleon-antinucleon ($\text{N}\text{N}$) system, leading to another $\text{N}\text{N}$ bound state. We use a realistic potential model to describe the medium- and long-range parts of the $\text{N}\text{N}$ interaction, and parametrize the short-range behavior. The general features of γ and π transitions, based on the selection rules, are emphasized. We illustrate these features with typical results for several choices of the short-range cutoff. The observation of pions is a necessary supplement to the γ-ray experiments, in order to significantly constrain the possible quantum number assignments of final states. We investigate transitions between quasiatomic (QA) and more deeply bound quasinuclear (QN) states, and also QN to QN γ or π emission. The former may have been seen in experiments involving the $\text{p}\text{p}$ atom, while the latter are in some optimum cases accessible in $\text{p}\text{d}$ spectator experiments, although there is no evidence for these QN to QN transitions as yet. The role of isospin mixing in QA states is discussed, as well as the importance of maintaining orthogonality of the QA and QN wave functions.     

Theory of four-dimensional fractional quantum Hall states

We propose a pseudo-potential Hamiltonian for the Zhang-Hu’s generalized fractional quantum Hall states to be the exact and unique ground states. Analogously to Laughlin’s quasi-hole (quasi-particle), the excitations in the generalized fractional quantum Hall states are extended objects. They are vortex-like excitations with fractional charges +(−)1/m³ in the total configuration space CP³. The density correlation function of the Zhang-Hu states indicates that they are incompressible liquid.     

Avoidance of counter-example to non-abelian Bloch-Nordsieck conjecture by using coherent state approach

It is shown that the counter-example to the non-abelian Bloch-Nordsieck conjecture in “$\text{q}\text{+}\text{q}\text{→ γ}{}^1\text{+}\text{soft gluons}$” to order α_s² is avoided at the cross section level if the initial st prepared according to the coherent state approach for treatment of the infrared region of non-abelian gauge theories.     

Stable hierarchical quantum Hall fluids as W1+∞ minimal models

In this paper, we pursue our analysis of the W_1+∞ symmetry of the low-energy edge excitations of incompressible quantum Hall fluids. These excitations are described by (1 + 1)-dimensional effective field theories, which are built by representations of the W_1+∞ algebra. Generic W_1+∞ theories predict many more fluids than the few, stable ones found in experiments. Here we identify a particular class of W_1+∞ theories, the minimal models, which are made of degenerate representations only - a familiar construction in conformal field theory. The W_1+∞ minimal models exist for specific values of the fractional Hall conductivity, which nicely fit the experimental data and match the results of the Jain hierarchy of quantum Hall fluids. We thus obtain a new hierarchical construction, which is based uniquely on the concept of quantum incompressible fluid and is independent of Jain's approach and hypotheses. Furthermore, a surprising non-abelian structure is found in the W_1+∞ minimal models: they possess neutral quark-like excitations with SU(m) quantum numbers and non-abelian fractional statistics. The physical electron is made of anyon and quark excitations. We discuss some properties of these neutral excitations which could be seen in experiments and numerical simulations.