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N. Read

Publications and source records attributed to N. Read.

At least 73 records · Page 4Linked to original sources
arXiv2001

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.

cond-mat.mes-hall↗
arXiv2000

Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states

When the two-dimensional random-bond Ising model is represented as a noninteracting fermion problem, it has the same symmetries as an ensemble of random matrices known as class D. A nonlinear sigma model analysis of the latter in two dimensions has previously led to the prediction of a metallic phase, in which the fermion eigenstates at zero energy are extended. In this paper we argue that such behavior cannot occur in the random-bond Ising model, by showing that the Ising spin correlations in the metallic phase violate the bound on such correlations that results from the reality of the Ising couplings. Some types of disorder in spinless or spin-polarized p-wave superconductors and paired fractional quantum Hall states allow a mapping onto an Ising model with real but correlated bonds, and hence a metallic phase is not possible there either. It is further argued that vortex disorder, which is generic in the fractional quantum Hall applications, destroys the ordered or weak-pairing phase, in which nonabelian statistics is obtained in the pure case.

cond-mat.dis-nn↗
arXiv2000

Random-bond Ising model in two dimensions, the Nishimori line, and supersymmetry

We consider a classical random-bond Ising model (RBIM) with binary distribution of $\pm K$ bonds on the square lattice at finite temperature. In the phase diagram of this model there is the so-called Nishimori line which intersects the phase boundary at a multicritical point. It is known that the correlation functions obey many exact identities on this line. We use a supersymmetry method to treat the disorder. In this approach the transfer matrices of the model on the Nishimori line have an enhanced supersymmetry osp($2n+1|2n$), in contrast to the rest of the phase diagram, where the symmetry is osp($2n|2n$) (where $n$ is an arbitrary positive integer). An anisotropic limit of the model leads to a one-dimensional quantum Hamiltonian describing a chain of interacting superspins, which are irreducible representations of the osp($2n+1|2n$) superalgebra. By generalizing this superspin chain, we embed it into a wider class of models. These include other models that have been studied previously in one and two dimensions. We suggest that the multicritical behavior in two dimensions of a class of these generalized models (possibly not including the multicritical point in the RBIM itself) may be governed by a single fixed point, at which the supersymmetry is enhanced still further to osp($2n+2|2n$). This suggestion is supported by a calculation of the renormalization-group flows for the corresponding nonlinear sigma models at weak coupling.

cond-mat.dis-nn↗
arXiv2000

Comment on "Cooper instability of composite fermions"

We comment on the recent paper by Scarola, Park, and Jain [Nature v. 406, p. 863 (2000); cond-mat/0012030] on a trial wavefunction calculation of pairing in a fractional quantum Hall system at nu=5/2. We point out two errors that invalidate the claimed calculations of a binding energy for Cooper pairs and of an energy gap for charged excitations.

cond-mat.mes-hall↗
arXiv2000

Bilayer Quantum Hall States at $ν=1$ and Coulomb Drag

We consider a number of strongly-correlated quantum Hall states which are likely to be realized in bilayer quantum Hall systems at total Landau level filling fraction ${ν_T}=1$. One state, the $(3,3,-1)$ state, can occur as an instability of a compressible state in the large $d/l_B$ limit, where $d$ and $l_B$ are the interlayer distance and magnetic length, respectively. This state has a hierarchical descendent which is interlayer coherent. Another interlayer coherent state, which is expected in the small $d/l_B$ limit is the well-known Halperin $(1,1,1)$ state. Using the concept of composite fermion pairing, we discuss the wavefunctions which describe these states. We construct a phase diagram using the Chern-Simons Landau-Ginzburg theory and discuss the transitions between the various phases. We propose that the longitudinal and Hall drag resistivities can be used together with interlayer tunneling to experimentally distinguish these different quantum Hall states. Our work indicates the bilayer ${ν_T}=1$ quantum Hall phase diagram to be considerably richer than that assumed so far in the literature.

cond-mat.mes-hall↗
arXiv2000

Thermal metal in network models of a disordered two-dimensional superconductor

We study the universality class for localization which arises from models of non-interacting quasiparticles in disordered superconductors that have neither time-reversal nor spin-rotation symmetries. Two-dimensional systems in this category, which is known as class D, can display phases with three different types of quasiparticle dynamics: metallic, localized, or with a quantized (thermal) Hall conductance. Correspondingly, they can show a variety of delocalization transitions. We illustrate this behavior by investigating numerically the phase diagrams of network models with the appropriate symmetry, and for the first time show the appearance of the metallic phase.

cond-mat.mes-hall↗
arXiv2000

Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect

We analyze pairing of fermions in two dimensions for fully-gapped cases with broken parity (P) and time-reversal (T), especially cases in which the gap function is an orbital angular momentum ($l$) eigenstate, in particular $l=-1$ (p-wave, spinless or spin-triplet) and $l=-2$ (d-wave, spin-singlet). For $l\neq0$, these fall into two phases, weak and strong pairing, which may be distinguished topologically. In the cases with conserved spin, we derive explicitly the Hall conductivity for spin as the corresponding topological invariant. For the spinless p-wave case, the weak-pairing phase has a pair wavefunction that is asympototically the same as that in the Moore-Read (Pfaffian) quantum Hall state, and we argue that its other properties (edge states, quasihole and toroidal ground states) are also the same, indicating that nonabelian statistics is a {\em generic} property of such a paired phase. The strong-pairing phase is an abelian state, and the transition between the two phases involves a bulk Majorana fermion, the mass of which changes sign at the transition. For the d-wave case, we argue that the Haldane-Rezayi state is not the generic behavior of a phase but describes the asymptotics at the critical point between weak and strong pairing, and has gapless fermion excitations in the bulk. In this case the weak-pairing phase is an abelian phase which has been considered previously. In the p-wave case with an unbroken U(1) symmetry, which can be applied to the double layer quantum Hall problem, the weak-pairing phase has the properties of the 331 state, and with nonzero tunneling there is a transition to the Moore-Read phase. The effects of disorder on noninteracting quasiparticles are considered.

cond-mat.mes-hall↗
arXiv1999

Exact exponents for the spin quantum Hall transition

We consider the spin quantum Hall transition which may occur in disordered superconductors with unbroken SU(2) spin-rotation symmetry but broken time-reversal symmetry. Using supersymmetry, we map a model for this transition onto the two-dimensional percolation problem. The anisotropic limit is an sl(2|1) supersymmetric spin chain. The mapping gives exact values for critical exponents associated with disorder-averages of several observables in good agreement with recent numerical results.

cond-mat.mes-hall↗
arXiv1998

Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level

The Pfaffian quantum Hall states, which can be viewed as involving pairing either of spin-polarized electrons or of composite fermions, are generalized by finding the exact ground states of certain Hamiltonians with k+1-body interactions, for all integers k > 0. The remarkably simple wavefunctions of these states involve clusters of k particles, and are related to correlators of parafermion currents in two-dimensional conformal field theory. The k=2 case is the Pfaffian. For k > 1, the quasiparticle excitations of these systems are expected to possess nonabelian statistics, like those of the Pfaffian. For k=3, these ground states have large overlaps with the ground states of the (2-body) Coulomb-interaction Hamiltonian for electrons in the first excited Landau level at total filling factors ν=2+3/5, 2+2/5.

cond-mat.mes-hall↗
arXiv1998

Lowest-Landau-level theory of the quantum Hall effect: the Fermi-liquid-like state

A theory for a Fermi-liquid-like state in a system of charged bosons at filling factor one is developed, working in the lowest Landau level. The approach is based on a representation of the problem as fermions with a system of constraints, introduced by Pasquier and Haldane (unpublished). This makes the system a gauge theory with gauge algebra W_infty. The low-energy theory is analyzed based on Hartree-Fock and a corresponding conserving approximation. This is shown to be equivalent to introducing a gauge field, which at long wavelengths gives an infinite-coupling U(1) gauge theory, without a Chern-Simons term. The system is compressible, and the Fermi-liquid properties are similar, but not identical, to those in the previous U(1) Chern-Simons fermion theory. The fermions in the theory are effectively neutral but carry a dipole moment. The density-density response, longitudinal conductivity, and the current density are considered explicitly.

cond-mat.mes-hall↗
arXiv1997

Conductance and its universal fluctuations in the directed network model at the crossover to the quasi-one-dimensional regime

The directed network model describing chiral edge states on the surface of a cylindrical 3D quantum Hall system is known to map to a one-dimensional quantum ferromagnetic spin chain. Using the spin wave expansion for this chain, we determine the universal functions for the crossovers between the 2D chiral metallic and 1D metallic regimes in the mean and variance of the conductance along the cylinder, to first nontrivial order.

cond-mat.mes-hall↗
arXiv1997

Mesoscopic conductance and its fluctuations at non-zero Hall angle

We consider the bilocal conductivity tensor, the two-probe conductance and its fluctuations for a disordered phase-coherent two-dimensional system of non-interacting electrons in the presence of a magnetic field, including correctly the edge effects. Analytical results are obtained by perturbation theory in the limit $σ_{xx} \gg 1$. For mesoscopic systems the conduction process is dominated by diffusion but we show that, due to the lack of time-reversal symmetry, the boundary condition for diffusion is altered at the reflecting edges. Instead of the usual condition, that the derivative along the direction normal to the wall of the diffusing variable vanishes, the derivative at the Hall angle to the normal vanishes. We demonstrate the origin of this boundary condition from different starting points, using (i) a simplified Chalker-Coddington network model, (ii) the standard diagrammatic perturbation expansion, and (iii) the nonlinear sigma-model with the topological term, thus establishing connections between the different approaches. Further boundary effects are found in quantum interference phenomena. We evaluate the mean bilocal conductivity tensor $σ_{μν}(r,r')$, and the mean and variance of the conductance, to leading order in $1/σ_{xx}$ and to order $(σ_{xy}/σ_{xx})^2$, and find that the variance of the conductance increases with the Hall ratio. Thus the conductance fluctuations are no longer simply described by the unitary universality class of the $σ_{xy}=0$ case, but instead there is a one-parameter family of probability distributions. In the quasi-one-dimensional limit, the usual universal result for the conductance fluctuations of the unitary ensemble is recovered, in contrast to results of previous authors. Also, a long discussion of current conservation.

cond-mat.mes-hall↗
arXiv1996

Invariant structure of the hierarchy theory of fractional quantum Hall states with spin

We describe the invariant structure common to abelian fractional quantum Hall systems with spin. It appears in a generalization of the lattice description of the polarized hierarchy that encompasses both partially polarized and unpolarized ground state systems. We formulate, using the spin-charge decomposition, conditions that should be satisfied so that the description is SU(2) invariant. In the case of the spin- singlet hierarchy construction, we find that there are as many SU(2) symmetries as there are levels in the construction. We show the existence of a spin and charge lattice for the systems with spin. The ``gluing'' of the charge and spin degrees of freedom in their bulk is described by the gluing theory of lattices.

cond-mat.mes-hall↗
arXiv1996

Scaling and Crossover Functions for the Conductance in the Directed Network Model of Edge States

We consider the directed network (DN) of edge states on the surface of a cylinder of length L and circumference C. By mapping it to a ferromagnetic superspin chain, and using a scaling analysis, we show its equivalence to a one-dimensional supersymmetric nonlinear sigma model in the scaling limit, for any value of the ratio L/C, except for short systems where L is less than of order C^{1/2}. For the sigma model, the universal crossover functions for the conductance and its variance have been determined previously. We also show that the DN model can be mapped directly onto the random matrix (Fokker-Planck) approach to disordered quasi-one-dimensional wires, which implies that the entire distribution of the conductance is the same as in the latter system, for any value of L/C in the same scaling limit. The results of Chalker and Dohmen are explained quantitatively.

cond-mat.mes-hall↗
arXiv1996

Metallic spin glasses

Recent work on the zero temperature phases and phase transitions of strongly random electronic system is reviewed. The transition between the spin glass and quantum paramagnet is examined, for both metallic and insulating systems. Insight gained from the solution of infinite range models leads to a quantum field theory for the transition between a metallic quantum paramagnetic and a metallic spin glass. The finite temperature phase diagram is described and crossover functions are computed in mean field theory. A study of fluctuations about mean field leads to the formulation of scaling hypotheses.

cond-mat↗
arXiv1996

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 $ν=1/2$ 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.

cond-mat↗
arXiv1996

Spin-Peierls states of quantum antiferromagnets on the $Ca V_4 O_9$ lattice

We discuss the quantum paramagnetic phases of Heisenberg antiferromagnets on the 1/5-depleted square lattice found in $Ca V_4 O_9$. The possible phases of the quantum dimer model on this lattice are obtained by a mapping to a quantum-mechanical height model. In addition to the ``decoupled'' phases found earlier, we find a possible intermediate spin-Peierls phase with spontaneously-broken lattice symmetry. Experimental signatures of the different quantum paramagnetic phases are discussed.

cond-mat↗