Non-Abelian quantized Hall states of electrons at filling factors 12/5 and 13/5 in the first excited Landau level

We present results of extensive numerical calculations on the ground state of electrons in the first excited (n=1) Landau level with Coulomb interactions, and including non-zero thickness effects, for filling factors 12/5 and 13/5 in the torus geometry. In a region that includes these experimentally-relevant values, we find that the energy spectrum and the overlaps with the trial states support the previous hypothesis that the system is in the non-Abelian k = 3 liquid phase we introduced in a previous paper.Comment: 5 pages (Revtex4), 7 figure

Incompressible liquid state of rapidly-rotating bosons at filling factor 3/2

Bosons in the lowest Landau level, such as rapidly-rotating cold trapped atoms, are investigated numerically in the specially interesting case in which the filling factor (ratio of particle number to vortex number) is 3/2. When a moderate amount of a longer-range (e.g. dipolar) interaction is included, we find clear evidence that the ground state is in a phase constructed earlier by two of us, in which excitations possess non-Abelian statistics.Comment: 5 pages, 5 figure

Real-space entanglement spectrum of quantum Hall systems

We study the real-space entanglement spectrum for fractional quantum Hall systems, which maintains locality along the spatial cut, and provide evidence that it possesses a scaling property. We also consider the closely-related particle entanglement spectrum, and carry out the Schmidt decomposition of the Laughlin state analytically at large size.Comment: 5 pages, 4 figures. V2: a bit more on non-locality of OP. V3: typos corrected; as publishe

Quasiholes and fermionic zero modes of paired fractional quantum Hall states: the mechanism for nonabelian statistics

The quasihole states of several paired states, the Pfaffian, Haldane-Rezayi, and 331 states, which under certain conditions may describe electrons at filling factor $\nu=1/2$ or 5/2, are studied, analytically and numerically, in the spherical geometry, for the Hamiltonians for which the ground states are known exactly. We also find all the ground states (without quasiparticles) of these systems in the toroidal geometry. In each case, a complete set of linearly-independent functions that are energy eigenstates of zero energy is found explicitly. For fixed positions of the quasiholes, the number of linearly-independent states is $2^{n-1}$ for the Pfaffian, $2^{2n-3}$ for the Haldane-Rezayi state; these degeneracies are needed if these systems are to possess nonabelian statistics, and they agree with predictions based on conformal field theory. The dimensions of the spaces of states for each number of quasiholes agree with numerical results for moderate system sizes. The effects of tunneling and of the Zeeman term are discussed for the 331 and Haldane-Rezayi states, as well as the relation to Laughlin states of electron pairs. A model introduced by Ho, which was supposed to connect the 331 and Pfaffian states, is found to have the same degeneracies of zero-energy states as the 331 state, except at its Pfaffian point where it is much more highly degenerate than either the 331 or the Pfaffian. We introduce a modification of the model which has the degeneracies of the 331 state everywhere including the Pfaffian point; at the latter point, tunneling reduces the degeneracies to those of the Pfaffian state. An experimental difference is pointed out between the Laughlin states of electron pairs and the other paired states, in the current-voltage response when electrons tunnel into the edge. And there's more.Comment: 43 pages, requires RevTeX. The 14 figures and 2 tables are available on request at [email protected] (include mailing address

SU(N) Quantum Hall Skyrmions

We have investigated skyrmions in N-component quantum Hall systems. We find that SU(N) skyrmions are the lowest energy charged excitations for filling factors \nu = 1,2,...,N-1 for small enough symmetry breaking terms. N>2 skyrmions can be realized in Si QH systems based on the (110) or (111) interfaces of Si, or perhaps in Si (100) systems, where the spin and valley isospin together provide an SU(4)-symmetry, or in multilayer QH systems. We also present Hartree-Fock results for a phenomenological easy-axis SU(2)-breaking model appropriate to valley degeneracy.Comment: 5 pages, 2 figure

Field theory of spin-singlet quantum Hall states

We formulate a field theory for a class of spin-singlet quantum Hall states (the Haldane-Rezayi state and its variants) which have been proposed for the quantized Hall plateaus observed at the second lowest Landau level. A new essential ingredient is a class of super Chern-Simons field. We show that the known properties of the states are consistently described by it. We also give a 2+1 dimensional hierarchical construction. Implications of the proposal are discussed and a new physical picture of composite particles at the second lowest Landau level emerges.Comment: RevTex, 5 pages, 1 figur

Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems

The Hall viscosity, a non-dissipative transport coefficient analogous to Hall conductivity, is considered for quantum fluids in gapped or topological phases. The relation to mean orbital spin per particle discovered in previous work by one of us is elucidated with the help of examples, using the geometry of shear transformations and rotations. For non-interacting particles in a magnetic field, there are several ways to derive the result (even at non-zero temperature), including standard linear response theory. Arguments for the quantization, and the robustness of Hall viscosity to small changes in the Hamiltonian that preserve rotational invariance, are given. Numerical calculations of adiabatic transport are performed to check the predictions for quantum Hall systems, with excellent agreement for trial states. The coefficient of k^4 in the static structure factor is also considered, and shown to be exactly related to the orbital spin and robust to perturbations in rotation invariant systems also.Comment: v2: Now 30 pages, 10 figures; new calculation using disk geometry; some other improvements; no change in result

Bulk and edge correlations in the compressible half-filled quantum Hall state

We study bulk and edge correlations in the compressible half-filled state, using a modified version of the plasma analogy. The corresponding plasma has anomalously weak screening properties, and as a consequence we find that the correlations along the edge do not decay algebraically as in the Laughlin (incompressible) case, while the bulk correlations decay in the same way. The results suggest that due to the strong coupling between charged modes on the edge and the neutral Fermions in the bulk, reflected by the weak screening in the plasma analogue, the (attractive) correlation hole is not well defined on the edge. Hence, the system there can be modeled as a free Fermi gas of {\em electrons} (with an appropriate boundary condition). We finally comment on a possible scenario, in which the Laughlin-like dynamical edge correlations may nevertheless be realized.Comment: package now includes the file epsfig.sty, needed to incorporate properly the 8 magnificent figure

Separation of spin and charge in paired spin-singlet quantum Hall states

We propose a series of paired spin-singlet quantum Hall states, which exhibit a separation of spin and charge degrees of freedom. The fundamental excitations over these states, which have filling fraction \nu=2/(2m+1) with m an odd integer, are spinons (spin-1/2 and charge zero) or fractional holons (charge +/- 1/(2m+1) and spin zero). The braid statistics of these excitations are non-abelian. The mechanism for the separation of spin and charge in these states is topological: spin and charge excitations are liberated by binding to a vortex in a p-wave pairing condensate. We briefly discuss related, abelian spin-singlet states and possible transitions.Comment: 4 pages, uses revtex

Edge of a Half-Filled Landau Level

We have investigated the electron occupation number of the edge of a quantum Hall (QH) droplet at $\nu=1/2$ using exact diagonalization technique and composite fermion trial wavefunction. We find that the electron occupation numbers near the edge obey a scaling behavior. The scaling result indicates the existence of a well-defined edge corresponding to the radius of a compact droplet of uniform filling factor 1/2. We find that the occupation number beyond this edge point is substantial, which is qualitatively different from the case of odd-denominator QH states. We relate these features to the different ways in which composite fermions occupy Landau levels for odd and even denominator states.Comment: To appear in Phys. Rev.