Results from exact diagonalization show that the spin-polarized Coulomb ground state at nu=5/2 is adiabatically connected with the Moore-Read wave function for systems with up to Nel = 16 electrons on the surface of a sphere. Varying the Haldane pseudopotentials v1 and v3, keeping all others at their value for Coulomb interaction, energy gap and (v1,v3)-dependent ground state overlap with the Moore-Read state form two ridges whose peak positions and extent in the (v1,v3)-plane essentially coincide. Thus, the physics of the Coulomb ground state at nu=5/2 is indeed captured by the Moore-Read state and that non-Abelian statistics can be expected under experimental conditions. Such adiabatic connection is not observed at nu=1/2, unless the width of the interface wave function and/or Landau level mixing effects are sufficiently large. Varying the width, an excitation gap is found for all system sizes Nel \le 18 studied. However, its system size dependence casts doubt on the existence of a Moore-Read-phase at nu=1/2 in the thermodynamic limit.
We examine the possibility of creating the Moore-Read Pfaffian in the lowest Landau level when the multicomponent Halperin 331 state (believed to describe quantum Hall bilayers and wide quantum wells at the filling factor $ν=1/2$) is destroyed by the increase of tunneling. Using exact diagonalization of the bilayer Hamiltonian with short-range and long-range (Coulomb) interactions in spherical and periodic rectangular geometries, we establish that tunneling is a perturbation that drives the 331 state into a compressible composite Fermi liquid, with the possibility for an intermediate critical …
We calculate the electron spectral functions at the edges of the Moore-Read Pfaffian and anti-Pfaffian fractional quantum Hall states, in the clean limit. We show that their qualitative differences can be probed using momentum resolved tunneling, thus providing a method to unambiguously distinguish which one is realized in the fractional quantum Hall state observed at filling factor $ν=5/2$. We further argue that edge reconstruction, which may be less important in the first excited Landau level (LL) than in the lowest LL, can also be detected this way if present.
We present a method for the exact construction of the fully particle-hole symmetric PH-Pfaffian ground state and its charged excitations on a sphere. We adopt the Moore-Read state, but with a nonholomorphic pairing component as in previous studies, and project it to the lowest Landau level. We study the energetics as well as other properties of these states and find that in a pure system interacting with the Coulomb forces the PH-Pfaffian cannot compete with either the Moore-Read state or its particle-hole conjugate, the anti-Pfaffian state, as an explanation for the 5/2-effect.
We find the finite-width, i.e., the layer thickness, of experimental quasi-two dimensional systems produces a physical environment sufficient to stabilize the Moore-Read Pfaffian state thought to describe the fractional quantum Hall effect at filling factor $ν=5/2$. This conclusion is based on exact calculations performed in the spherical and torus geometries, studying wavefunction overlap and ground state degeneracy
We examine the quantum phase diagram of the fractional quantum Hall effect (FQHE) in the lowest two Landau levels in half-filled bilayer structures as a function of tunneling strength and layer separation, i.e., we revisit the lowest Landau level filling factor 1/2 bilayer problem and make new predictions involving bilayers in the half-filled second Landau level (i.e., filling factor 5/2). Using numerical exact diagonalization we investigate the important question of whether this system supports a FQHE described by the non-Abelian Moore-Read Pfaffian state in the strong tunneling regime. In th…
We consider the properties of the Moore-Read Pfaffian state under particle-hole conjugation. We show that the particle-hole conjugate of the Pfaffian state - or "anti-Pfaffian" state - is in a different universality class from the Pfaffian state, with different topological order. The two states can be distinguished by both their bulk and edge physics though the difference is most dramatic at the edge: the edge of the anti-Pfaffian state has a composite structure that leads to a different thermal Hall conductance and different tunneling exponents than the Pfaffian state. At the same time, the t…
We numerically assess model wave functions for the recently proposed particle-hole-symmetric Pfaffian (`PH-Pfaffian') topological order, a phase consistent with the recently reported thermal Hall conductance [Banerjee et al., Nature 559, 205 (2018)] at the ever enigmatic $ν=5/2$ quantum-Hall plateau. We find that the most natural Moore-Read-inspired trial state for the PH-Pfaffian, when projected into the lowest Landau level, exhibits a remarkable numerical similarity on accessible system sizes with the corresponding (compressible) composite Fermi liquid. Consequently, this PH-Pfaffian trial s…
We analyze the Moore-Read Pfaffian state on a thin torus. The known six-fold degeneracy is realized by two inequivalent crystalline states with a four- and two-fold degeneracy respectively. The fundamental quasihole and quasiparticle excitations are domain walls between these vacua, and simple counting arguments give a Hilbert space of dimension $2^{n-1}$ for $2n-k$ holes and $k$ particles at fixed positions and assign each a charge $\pm e/4$. This generalizes the known properties of the hole excitations in the Pfaffian state as deduced using conformal field theory techniques. Numerical calcul…
We consider a quaternately generalized Pfaffian QGPf$(\frac{1}{J(z_i,z_j,z_k,z_l)})[J(z_1,...,z_N)]^2$ in which the square of Vandermonde determinant, $[J(z_1,...,z_N)]^2$, implies the upmost Landau level is half filled. This wave function is the unique highest density zero energy state of a special short range interacting Hamiltonian. One can think this quaternate composite fermion liquid as a competing ground state of Moore-Read (MR) Pfaffian state at $ν=5/2$. The degeneracy of the quasihole excitations above the QGPf is higher than that of Moore-Read even Read-Rezayi quasiholes. The QGPf is…
We study charged spin textures (CST) over the Moore-Read quantum Hall state at filling factor 5/2. We develop an algebraic framework and show that the pairing condition that is inherent in the Moore-Read state naturally leads to a class of charged spin textures, labeled by winding numbers [w_I, w_II]. The fundamental CST, with labels [1,0] and electric charge e/4, is identified with the polar core vortex known in the spin-1 BEC literature. The spin texture carried by the fusion product of fundamental CSTs is correlated with the fusion channel of the underlying non-Abelian quasiholes.
Coupled atom-cavity arrays, such as those described by the Jaynes-Cummings Hubbard model, have the potential to emulate a wide range of condensed matter phenomena. In particular, the strongly correlated states of the fractional quantum Hall effect can be realised. At some filling fractions, the fraction quantum Hall effect has been shown to possess ground states with non-abelian excitations. The most well studied of these states is the Pfaffian state of Moore and Read, which is the groundstate of a Hall Liquid with a 3-body interaction. In this paper we show how an effective 3-body interaction…
We present a comprehensive numerical study of a microscopic model of the fractional quantum Hall system at filling fraction $ν= 5/2$, based on the disc geometry. Our model includes Coulomb interaction and a semi-realistic confining potential. We also mix in some three-body interaction in some cases to help elucidate the physics. We obtain a phase diagram, discuss the conditions under which the ground state can be described by the Moore-Read state, and study its competition with neighboring stripe phases. We also study quasihole excitations and edge excitations in the Moore-Read--like state. Fr…
We study charged excitations of the non-abelian Moore-Read liquid at filling factor nu=5/2, allowing for spin depolarization. Using a combination of numerical studies, and taking account of non-zero well widths, we find that at sufficiently low Zeeman energy it is energetically favourable for charge e/4 quasiholes to bind into "skyrmions" of charge e/2. We show that skyrmion formation is further promoted by disorder, and argue that this can lead to a depolarized nu=5/2 ground state in realistic experimental situations. We comment on the consequences for the activated transport.
We present evidence supporting the weakly paired Moore-Read phase in the half-filled second Landau level, focusing on some of the qualitative features of its excitations. Based on numerical studies, we show that systems with odd particle number at the flux $N_ϕ=2N-3$ can be interpreted as a neutral fermion mode of one unpaired fermion, which is gapped. The mode is found to have two distinct minima, providing a signature that could be observed by photoluminescence. In the presence of two quasiparticles the same neutral fermion excitation is shown to be gapless, confirming expectations for non-A…
We study the nature of the ν=5/2 quantum Hall state in wide quantum wells under the mixing of electronic subbands and Landau levels. We introduce a general method to analyze the Moore-Read Pfaffian state and its particle-hole conjugate, the anti-Pfaffian, under periodic boundary conditions in a "quartered" Brillouin zone scheme containing both even and odd numbers of electrons. We examine the rotational quantum numbers on the torus, and show spontaneous breaking of the particle-hole symmetry can be observed in finite-size systems. In the presence of electronic-subband and Landau-level mixing t…
We calculate the dynamical structure factor of the ν=5/2 non-abelian quantum Hall state in the dipole approximation, valid for large momenta. Due to the fact that both quasi-particles (qps) and quasi-holes (qhs) have an internal Majorana degree of freedom, a qp-qh pair has a fermionic degree of freedom which can be either empty or occupied, and leads to a splitting of the roton mode. Observation of this splitting by means of finite wavelength optical spectroscopy could provide evidence for Majorana modes in the ν=5/2 quantum Hall state.
We use conformal field theory to construct model wavefunctions for a gapless interface between lattice versions of a bosonic Laughlin state and a fermionic Moore-Read state, both at $ν=1/2$. The properties of the resulting model state, such as particle density, correlation function and Rényi entanglement entropy are then studied using the Monte Carlo approach. Moreover, we construct the wavefunctions also for anyonic excitations (quasiparticles and quasiholes). We study their density profile, charge and statistics. We show that, similarly to the Laughlin-Laughlin case studied earlier, some any…
We investigate, with the help of Monte-Carlo and exact-diagonalization calculations in the spherical geometry, several compressible and incompressible candidate wave functions for the recently observed quantum Hall state at the filling factor $ν=1/4$ in a wide quantum well. The quantum well is modeled as a two-component system by retaining its two lowest subbands. We make a direct connection with the phenomenological effective-bilayer model, which is commonly used in the description of a wide quantum well, and we compare our findings with the established results at $ν=1/2$ in the lowest Landau…
We develop a proposal to realise a widely tunable and clean quantum phase transition in bilayer graphene between two paradigmatic fractionalized phases of matter: the Moore-Read fractional quantum Hall state and the composite Fermi liquid metal. This transition can be realized at total fillings $ν=\pm 3+1/2$ and the critical point can be controllably accessed by tuning either the interlayer electric bias or the perpendicular magnetic field values over a wide range of parameters. We study the transition numerically within a model that contains all leading single particle corrections to the band…
We study the non-Abelian statistics of quasiparticles in the Ising-type quantum Hall states which are likely candidates to explain the observed Hall conductivity plateaus in the second Landau level, most notably the one at filling fraction nu=5/2. We complete the program started in Nucl. Phys. B 506, 685 (1997) and show that the degenerate four-quasihole and six-quasihole wavefunctions of the Moore-Read Pfaffian state are orthogonal with equal constant norms in the basis given by conformal blocks in a c=1+1/2 conformal field theory. As a consequence, this proves that the non-Abelian statistics…
We report on results of numerical studies of the spin polarization of the half filled second Landau level, which corresponds to the fractional quantum Hall state at filling factor $ν=5/2$. Our studies are performed using both exact diagonalization and Density Matrix Renormalization Group (DMRG) on the sphere. We find that for the Coulomb interaction the exact finite-system ground state is fully polarized, for shifts corresponding to both the Moore-Read Pfaffian state and its particle-hole conjugate (anti-Pfaffian). This result is found to be robust against small variations of the interaction. …
The essence of the $ν=5/2$ fractional quantum Hall effect is believed to be well captured by the Moore-Read Pfaffian (or anti-Pfaffian) description. However, an important mystery regarding the formation of the Pfaffian state is the role of the three-body interaction Hamiltonian $H_3$ that produces the Pfaffian as an exact ground state and the concomitant particle-hole symmetry breaking. We show that a two-body interaction Hamiltonian $H_2$ constructed via particle-hole symmetrization of $H_3$ produces a ground state nearly exactly approximating the Pfaffian and anti-Pfaffian states, respective…
Interesting non-Abelian states, e.g., the Moore-Read Pfaffian and the anti-Pfaffian, offer candidate descriptions of the $ν= 5/2$ fractional quantum Hall state. But the significant controversy surrounding the nature of the $ν= 5/2$ state has been hampered by the fact that the competition between these and other states is affected by small parameter changes. To study the phase diagram of the $ν= 5/2$ state we numerically diagonalize a comprehensive effective Hamiltonian describing the fractional quantum Hall effect of electrons under realistic conditions in GaAs semiconductors. The effective Ha…
The coupled-wire construction provides a useful way to obtain microscopic Hamiltonians for various two-dimensional topological phases, among which fractional quantum Hall states are paradigmatic examples. Using the recently introduced flux attachment and vortex duality transformations for coupled wires, we show that this construction is remarkably versatile to encapsulate phenomenologies of hierarchical quantum Hall states: the Jain-type hierarchy states of composite fermions filling Landau levels and the Haldane-Halperin hierarchy states of quasiparticle condensation. The particle-hole conjug…
A theory is developed for the paired even-denominator fractional quantum Hall states in the lowest Landau level. We show that electrons bind to quantized vortices to form composite fermions, interacting through an exact instantaneous interaction that favors chiral p-wave pairing. Two canonically dual pairing gap functions are related by the bosonic Laughlin wavefunction (Jastraw factor) due to the correlation holes. We find that the ground state is the Moore-Read pfaffian in the long wavelength limit for weak Coulomb interactions, a new pfaffian of an oscillatory pairing function for intermedi…
We introduce a family of strongly-correlated spin wave functions on arbitrary spin-1/2 and spin-1 lattices in one and two dimensions. These states are lattice analogues of Moore-Read states of particles at filling fraction 1/q, which are non-Abelian Fractional Quantum Hall states in 2D. One parameter enables us to perform an interpolation between the continuum limit, where the states become continuum Moore-Read states of bosons (odd q) and fermions (even q), and the lattice limit. We show numerical evidence that the topological entanglement entropy stays the same along the interpolation for so…
Based on the recently proposed SUSY quantum Hall effect, we show that Laughlin and Moore-Read states are related by a hidden SUSY transformation. Regarding the SUSY Laughlin wavefunction as a master wavefunction, Laughlin and Moore-Read states appear as two extreme limits of component wavefunctions. Realizations of topological excitations on Laughlin and Moore-Read states are also discussed in the SUSY formalism. We develop a streographically projected formulation of the SUSY quantum Hall effect. With appropriate interpretation of Grassmann odd coordinates, we illustrate striking analogies bet…
In search of states with non-Abelian statistics, we explore the fractional quantum Hall effect in a system of two-dimensional charge carrier holes. We propose a new method of mapping states of holes confined to a finite width quantum well in a perpendicular magnetic field to states in a spherical shell geometry. This method provides single-particle hole states used in exact diagonalization of systems with a small number of holes in the presence of Coulomb interactions. An incompressible fractional quantum Hall state emerges in a hole liquid at the half-filling of the ground state in a magnetic…
We study a quantum Hall bilayer system of bosons at total filling factor $ν= 1$, and study the phase that results from short ranged pair-tunneling combined with short ranged interlayer interactions. We introduce two exactly solvable model Hamiltonians which both yield the coupled Moore-Read state [Phys.~Rev.~Lett.~{\bf 108}, 256809 (2012)] as a ground state, when projected onto fixed particle numbers in each layer. One of these Hamiltonians describes a gapped topological phase while the other is gapless. However, on introduction of a pair tunneling term, the second system becomes gapped and de…
Two- and three-body correlations of incompressible quantum liquids are studied numerically. Pairing of composite fermions (CFs) in the 1/3-filled second CF Landau level is found at nu_e=4/11. It is explained by reduced short-range repulsion due to ring-like single-particle charge distribution. Although Moore-Read state of CFs is unstable in the 1/2-filled second CF level, condensation of its quasiholes is a possible origin of incompressibility at nu_e=4/11. Electron pairing occurs at nu_e=7/3 and 13/3, but with different pair-pair correlations. Signatures of triplets are found at higher fillin…
We propose noise oscillation measurements in a double point contact, accessible with current technology, to seek for a signature of the non-abelian nature of the ν=5/2 quantum Hall state. Calculating the voltage and temperature dependence of the current and noise oscillations, we predict the non-abelian nature to materialize through a multiplicity of the possible outcomes: two qualitatively different frequency dependences of the nonzero interference noise. Comparison between our predictions for the Moore-Read state with experiments on ν=5/2 will serve as a much needed test for the nature of th…
We construct the wave functions for the Moore-Read $ν= 5/2$ quantum Hall state on a torus in the presence of two quasiholes. These explicit wave functions allow us to compute the monodromy matrix that describes the effect of quasihole motion on the space of degenerate ground states. The result agrees with the recent discussion by Oshikawa {\it et al.} Our calculation provides a conformal field theory explanation of why certain transitions between ground states are forbidden. It is because taking a quasihole around a generator of the torus can change the fusion channel of the two quasiholes, an…
We study the ground state and low-energy excitations of fractional quantum Hall systems on a disk at filling fraction $ν= 5/2$, with Coulomb interaction and background confining potential. We find the Moore-Read ground state is stable within a finite but narrow window in parameter space. The corresponding low-energy excitations contain a fermionic branch and a bosonic branch, with widely different velocities. A short-range repulsive potential can stabilize a charge $+e/4$ quasihole at the center, leading to a different edge excitation spectrum due to the change of boundary conditions for Major…
Motivated by the recent work of QED$_3$-Chern-Simons quantum critical points of fractional Chern insulators (Phys. Rev. X \textbf{8}, 031015, (2018)), we study its non-Abelian generalizations, namely QCD$_3$-Chern-Simons quantum phase transitions of fractional Chern insulators. These phase transitions are described by Dirac fermions interacting with non-Abelian Chern-Simons gauge fields ($U(N)$, $SU(N)$, $USp(N)$, etc.). Utilizing the level-rank duality of Chern-Simons gauge theory and non-Abelian parton constructions, we discuss two types of QCD$_3$ quantum phase transitions. The first type h…
We compare ground state energies by variational Monte Carlo of the spin unpolarized Halperin 331 and the spin polarized Moore-Read (MR) Pfaffian fractional quantum Hall states at half-filling of the lowest Landau level (LLL) and the second Landau level (SLL) as a function of small deviations around the Coulomb point via the finite thickness effect and direct alterations to the the first two Haldane pseudopotentials. In the comparison we find that in the LLL, either the 331 state or the MR Pfaffian may be lower in energy depending on the deviations. In the SLL, however, the MR Pfaffian is consi…
We analyze transitions between quantum Hall ground states at prominent filling factors $ν$ in the spherical geometry by tuning the width parameter of the Zhang-Das Sarma interaction potential. We find that incompressible ground states evolve adiabatically under this tuning, whereas the compressible ones are driven through a first order phase transition. Overlap calculations show that the resulting phase is increasingly well described by appropriate analytic model wavefunctions (Laughlin, Moore-Read, Read-Rezayi). This scenario is shared by both odd ($ν=1/3, 1/5, 3/5, 7/3, 11/5, 13/5$) and even…
In fractional quantum Hall systems, quasiparticles of fractional charge can tunnel between the edges at a quantum point contact. Such tunneling (or backscattering) processes contribute to charge transport, and provide information on both the charge and statistics of the quasiparticles involved. Here we study quasiparticle tunneling in the Moore-Read state, in which quasiparticles of charge e/4 (non-Abelian) and e/2 (Abelian) may co-exist and both contribute to edge transport. On a disk geometry, we calculate the matrix elements for e/2 and e/4 quasiholes to tunnel through the bulk of the Moore…
We study a quantum point contact in the fractional quantum Hall regime at Landau level filling factors 1/3 and 5/2. By using exact diagonalizations in the cylinder geometry we identify the edge modes in the presence of a parabolic confining potential. By changing the sign of the potential we can access both the tunneling through the bulk of the fluid and the tunneling between spatially separated droplets. This geometry is realized in the quantum point contact geometry for two-dimensional electron gases. In the case of the model Moore-Read Pfaffian state at filling factor 5/2 we identify the co…
We present a physical construction of degenerate groundstates of the Moore-Read Pfaffian states, which exhibits non-Abelian statistics, on general Riemann surface with genus g. The construction is given by a generalization of the recent argument [M.O. and T. Senthil, Phys. Rev. Lett. 96, 060601 (2006)] which relates fraction- alization and topological order. The nontrivial groundstate degeneracy obtained by Read and Green [Phys. Rev. B 61, 10267 (2000)] based on differential geometry is reproduced exactly. Some restrictions on the statistics, due to the fractional charge of the quasiparticle a…
Two- and three-body correlations in partially filled degenerate fermion shells are studied numerically for various interactions between the particles. Three distinct correlation regimes are defined, depending on the short-range behavior of the pair pseudopotential. For pseudopotentials similar to those of electrons in the first excited Landau level, correlations at half-filling have a simple three-body form consisting of the maximum avoidance of the triplet state with the smallest relative angular momentum R_3=3. In analogy to the superharmonic criterion for Laughlin two-body correlations, the…
A supersymmetric Hamiltonian is constructed for the edge excitations of the Moore-Read (Pfaffian) like state, which is a realization of the N=2 supersymmetric CS model. Fermionic generators and their conjugates are introduced to deal with the fermion pairing, whose condensation form a BCS like state. After Bogoliubov transformation, a N=2 supersymmetric and nonrelativistic Hamiltonian is found to take a known form, which is integrable. The main difference between the Moore-Read state and our BCS like state is that the number of fermion pairs in our formalism is not fixed. However, we have also…
We demonstrate numerically that non-Abelian quasihole excitations of the $ν= 5/2$ fractional quantum Hall state have some of the key properties necessary to support quantum computation. We find that as the quasihole spacing is increased, the unitary transformation which describes winding two quasiholes around each other converges exponentially to its asymptotic limit and that the two orthogonal wavefunctions describing a system with four quasiholes become exponentially degenerate. We calculate the length scales for these two decays to be $ξ_{U} \approx 2.7 \ell_0$ and $ξ_{E} \approx 2.3 \ell_0…
We report the observation of developing fractional quantum Hall states at Landau level filling factors $ν= 1/2$ and 1/4 in electron systems confined to wide GaAs quantum wells with significantly $asymmetric$ charge distributions. The very large electric subband separation and the highly asymmetric charge distribution at which we observe these quantum Hall states, together with the fact that they disappear when the charge distribution is made symmetric, suggest that these are one-component states, possibly described by the Moore-Read Pfaffian wavefunction.
The Moore-Read state is one the most well known non-Abelian fractional quantum Hall states. It supports non-Abelian Ising anyons in the bulk and a chiral bosonic and chiral Majorana modes on the boundary. It has been recently conjectured that these modes are superpartners of each other and described by a supersymmetric conformal field theory [1]. We propose a non-relativistic supergeometric theory that is compatible with this picture and gives rise to an effective spin-3/2 field in the bulk. After breaking supersymmetry through a Goldstino, the spin-3/2 field becomes massive and can be seen as…
Nature of the fractional quantum Hall state at Landau level filling factor 5/2 remains elusive despite intensive experimental and theoretical work. While the leading theoretical candidates are Moore-Read Pfaffian (Pf) and its particle-hole conjugate anti-Pfaffian (APf), neither received unambiguous experimental support. We show that a state that is intermediate between them, made of alternating stripes of Pf and APf in the bulk, is a viable candidate. Such a state is shown to be incompressible and thus a charge insulator in the bulk, but a heat conductor due to the presence of gapless neutral …
We examine the quantum phase diagram of the fractional quantum Hall effect in the lowest Landau level in half-filled bilayer structures as a function of tunneling strength and layer separation. Using numerical exact diagonalization we investigate the important question of whether this system supports a fractional quantum Hall effect described by the non-Abelian Moore-Read Pfaffian state in the strong tunneling regime. We find that, although it is in principle possible, it is unlikely that the non-Abelian FQHE exists in the lowest Landau level. We establish that all so far observed FQHE states …
We construct a wavefunction, generalizing the well known Moore-Read Pfaffian, that describes spinless electrons at filling fraction nu=2/5 (or bosons at filling fraction nu=2/3) as the ground state of a very simple three body potential. We find, analogous to the Pfaffian, that when quasiholes are added there is a ground state degeneracy which can be identified as zero-modes of the quasiholes. The zero-modes are identified as having semionic statistics. We write this wavefunction as a correlator of the Virasoro minimal model conformal field theory M(5,3). Since this model is non-unitary, we con…
We construct an exactly soluble spin-$\frac{1}2$ model on a honeycomb lattice, which is a generalization of Kitaev model. The topological phases of the system are analyzed by study of the ground state sector of this model, the vortex-free states. Basically, there are two phases, A phase and B phase. The behaviors of both A and B phases may be studied by mapping the ground state sector into a general p-wave paired states of spinless fermions with tunable pairing parameters on a square lattice. In this p-wave paired state theory, the A phase is shown to be the strong paired phase, an insulating …
Significant insights into non-Abelian quantum Hall states were obtained from studying special multi-particle interaction Hamiltonians, whose unique ground states are the Moore-Read and Read-Rezayi states for the case of spinless electrons. We generalize this approach to include the electronic spin-1/2 degree of freedom. We demonstrate that in the absence of Zeeman splitting the ground states of such Hamiltonians have large degeneracies and very rich spin structures. The spin structure of the ground states and low-energy excitations can be understood based on an emergent SU(3) symmetry for the …
We show that cotunneling in the 5/2 fractional quantum Hall regime allows us to test the Moore-Read wave function, proposed for this regime, and to probe the nature of the fractional charge carriers. We calculate the cotunneling current for electrons that tunnel between two quantum Hall edge states via a quantum dot and for quasiparticles with fractional charges e/4 and e/2 that tunnel via an antidot. While electron cotunneling is strongly suppressed, the quasiparticle tunneling shows signatures characteristic of the Moore-Read state. For comparison, we also consider cotunneling between Laughl…
Non-Abelian excitations are an interesting feature of many fractional quantum Hall phases, including those phases described by the Moore-Read (or Pfaffian) wave function. However, the detection of the non-Abelian quasiparticles is challenging. Here, we consider a system described by the Moore-Read wave function, and assume that impurity particles bind to its quasiholes. Then, the angular momentum of the impurities, reflected also by the impurity density, provides a useful witness of the physics of the non-Abelian excitations. By demanding that the impurities are constrained to the lowest Landa…
Certain well known quantum Hall states -- including the Laughlin states, the Moore-Read Pfaffian, and the Read-Rezayi Parafermion states -- can be defined as the unique lowest degree symmetric analytic function that vanishes as at least p powers as some number (g+1) of particles approach the same point. Analogously, these same quantum Hall states can be generated as the exact highest density zero energy state of simple angular momentum projection operators. Following this theme we determine the highest density zero energy state for many other values of p and g.
Two-dimensional semiconductor quantum dots are studied in the the filling-factor range 2<v<3. We find both theoretical and experimental evidence of a collective many-body phenomenon, where a fraction of the trapped electrons form an incompressible spin-droplet on the highest occupied Landau level. The phenomenon occurs only when the number of electrons in the quantum dot is larger than ~30. We find the onset of the spin-droplet regime at v=5/2. This proposes a finite-geometry alternative to the Moore-Read-type Pfaffian state of the bulk two-dimensional electron gas. Hence, the spin-droplet for…
Motivated by the physics of the Moore-Read ν= 1/2 state away from half-filling, we investigate collective states of non-abelian e/4 quasiparticles in a magnetic field. We consider two types of collective states: incompressible liquids and Wigner crystals. In the incompressible liquid case, we construct a natural series of states which can be thought of as a non-abelian generalization of the Laughlin states. These states are associated with a series of hierarchical states derived from the Moore-Read state - the simplest of which occur at filling fraction 8/17 and 7/13. Interestingly, we find th…
