The Hilbert spaces of the edge excitations of several "paired" fractional quantum Hall states, namely the Pfaffian, Haldane-Rezayi and 331 states, are constructed and the states at each angular momentum level are enumerated. The method is based on finding all the zero energy states for those Hamiltonians for which each of these known ground states is the exact, unique, zero-energy eigenstate of lowest angular momentum in the disk geometry. For each state, we find that, in addition to the usual bosonic charge-fluctuation excitations, there are fermionic edge excitations. The wavefunctions for each case have a similar form, related to Slater determinants, and the edge states satisfy a "projection rule", that the parity of the number of fermions added to the edge equals the parity of the charge added. The edge states can be built out of quantum fields that describe the fermions, in addition to the usual scalar bosons (or Luttinger liquids) that describe the charge fluctuations. The fermionic fields in the Pfaffian and 331 cases are a non-interacting Majorana (i.e., real Dirac) and Dirac field, respectively. For the Haldane-Rezayi state, the field is an anticommuting scalar. For this system we exhibit a chiral Lagrangian that has manifest SU(2) symmetry but breaks Lorentz invariance because of the breakdown of the spin statistics connection implied by the scalar nature of the field and the positive definite norm on the Hilbert space. Finally we consider systems on a cylinder where the fluid has two edges and construct the sectors of zero energy states, discuss the projection rules for combining states at the two edges, and calculate the partition function for each edge excitation system at finite temperature in the thermodynamic limit. The corresponding theory for the hierarchy and its generalizations is also given. It is pointed out that the conformal field theories for the edge states are examples of orbifold constructions. Two appendices contain technical details.

We present a simple new effective-field theory for the metallic state of a disordered interacting Fermi liquid, taking into account its instability towards the formation of local-moment states. We find a generalization of the compensation theorem of the single-impurity Anderson model, namely, that strongly localized magnetic instabilities occur even when the mean-field single-quasiparticle states are extended. The theory clarifies the understanding of recent thermodynamic and spin-resonance measurements in phosphorus-doped silicon.PACS numbers: 71.30. +H, 72.10.Fk, 75.20.Hr Many theoretical analyses 1,2 have recently addressed the subject of the metal-insulator transition (MIT) in a disordered interacting-electron gas. Using a renormalized weak-disorder perturbation theory, but including the effect of interactions exactly within lowest order in disorder, these investigations have led to an understanding of many transport properties in the disordered metallic phase. However, these theories remain unsatisfactory in explaining the low-temperature thermodynamics as well as the region near the MIT. 3 " 7 Here we present a new mean-field theory of the disordered metallic state. Our theory is directly motivated by experiments on doped semiconductors and should serve as an improved starting point for a complete theory of the MIT.We take a point of view that is complementary to recent approaches; 2 we treat the noninteracting disordered Hamiltonian exactly in a numerical calculation, but account for the interactions in a Hartree-Fock-type approximation. 8 Such an approach is crucial in accounting for the instability of an interacting-electron gas towards the formation of localized magnetic states. 9 This instability is not directly apparent in a disorder perturbation theory even though it can occur for weak disorder. Additional motivation comes from the understanding of the insulator through magnetic and optical measurements in doped semiconductors 10 where a correct treatment of disorder effects was crucial.We discuss our approach in the framework of a disordered Anderson-Hubbard model,where i,j extend over all the sites in the system (not necessarily on a lattice), «,

In bilayer quantum Hall systems at filling fractions near ν = 1/2 + 1/2, as the spacing d between the layers is continuously decreased, intra-layer correlations must be replaced by inter-layer correlations, and the composite fermion (CF) Fermi seas at large d must eventually be replaced by a composite boson (CB) condensate or "111 state" at small d. We propose a scenario where CBs and CFs coexist in two interpenetrating fluids in the transition. Trial wavefunctions describing these mixed CB-CF states compare very favorably with exact diagonalization results. A Chern-Simons transport theory is constructed that is compatible with experiment.Bilayer quantum Hall systems show a remarkable variety of phenomena [1]. Perhaps the most studied case is when the electron density in each of the two layers is such that ν = nφ 0 /B = 1 2 , where n is density, φ 0 = 2πhc/e is the flux quantum and B is the magnetic field perpendicular to the sample. At this filling fraction, it is known that at least two types of states can occur depending on the spacing d between the layers. For large d the two layers must be essentially independent ν = 1 2 states, which are thought to be well described as compressible composite fermion (CF) Fermi seas with strong intralayer correlations and no interlayer correlations [2]. For small enough values of d one should have an interlayer coherent "111 state" which can be described as a composite boson (CB) condensate with strong interlayer correlations and intralayer correlations which are weaker than that of the CF Fermi sea [1]. The nature of the transition between CFs and CBs is the focus of this paper. (Throughout this paper we will assume zero interlayer tunnelling, assume the spins are fully polarized, and set the in-plane field to zero.) Previous numerical work [4] suggested that the transition between the CF Fermi sea and the CB 111 state may be first order. (A number of more exotic mechanisms have also been proposed [5] . We are thus motivated to look for a more continuous transition from the CF Fermi liquid to the CB 111 state. The picture we have in mind is a family of states interpolating between these endpoints where each state is specified by the number of CFs and the number of CBs with the total number of CBs plus CFs remaining fixed. A first order transition could also be described as a mixture of CBs and CFs but with phase separation of the two fluids. Here we instead consider states where the CF and CB fluids interpenetrate. Since the wavefunction must be fully antisymmetric in terms of the original electrons, one might think of the electron having some CF character and some CB character. This interpolation between CF and CB is advantageous since it allows us (by varying the ratio of CFs to CBs) to construct states with varying degrees of inter-versus intra-layer correlations.We find that such mixed CF-CB states agree well with exact diagonalizations. Further, we find that a ChernSimons version of our mixed Bose-Fermi theory is consistent with experimental observation, and in partic...

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 level. At ν = 1/4, the overlap calculations for the Halperin (5,5,3) and (7,7,1) states, the generalized Haldane-Rezayi state and the Moore-Read Pfaffian, suggest that the incompressible state is likely to be realized in the interplay between the Halperin (5,5,3) state and the Moore-Read Pfaffian. Our numerics shows the latter to be very susceptible to changes in the interaction coefficients, thus indicating that the observed state is of multicomponent nature.

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 state that is reminiscent of the Moore-Read Pfaffian. These results are interpreted in the two-component BCS model for Cauchy pairing with a tunneling constraint. We comment on the conditions to be imposed on a system with fluctuating density in order to achieve the stable Pfaffian phase.