Behaviour of the energy gap near a commensurate-incommensurate transition in double layer quantum Hall systems at nu=1

The charged excitations in the system of the title are vortex-antivortex pairs in the spin-texture described in the theory by Yang et al which, in the commensurate phase, are bound together by a ``string''. It is shown that their excitation energy drops as the string lengthens as the parallel magnetic field approaches the critical value, then goes up again in the incommensurate phase. This produces a sharp downward cusp at the critical point. An alternative description based on the role of disorder in the tunnelling and which appears not to produce a minimum in the excitation energy is also discussed. It is suggested that a similar transition could also occur in compressible Fermi-liquid-like states.Comment: latex file, 17 page

The Hartree-Fock state for the 2DEG at filling factor 1/2 revisited: analytic solution, dynamics and correlation energy

The CDW Hartree-Fock state at half filling and half electron per unit cell is examined. Firstly, an exact solution in terms of Bloch-like states is presented. Using this solution we discuss the dynamics near half filling and show the mass to diverge logarithmically as this filling is approached. We also show how a uniform density state may be constructed from a linear combination of two degenerate solutions. Finally we show the second order correction to the energy to be an order of magnitude larger than that for competing CDW solutions with one electron per unit cell.Comment: 14 pages, no figures, extended acknowledgements, two new references include

Coulomb drag as a signature of the paired quantum Hall state

Motivated by the recent Coulomb drag experiment of M. P. Lilly et. al, we study the Coulomb drag in a two-layer system with Landau level filling factor $\nu=1/2$. We find that the drag conductivity in the incompressible paired quantum Hall state at zero temperature can be finite. The drag conductivity is also greatly enhanced above $T_c$, at which the transition between the weakly coupled compressible liquids and the paired quantum Hall liquid takes place. We discuss the implications of our results for the recent experiment.Comment: 4 pages, 1 figure included, replaced by the published versio

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.Comment: 21 pages, LaTex, Submitted to Phys. Rev.

Spin dynamics simulations of the magnetic dynamics of RbMnF3_3 and direct comparison with experiment

Spin-dynamics techniques have been used to perform large-scale simulations of the dynamic behavior of the classical Heisenberg antiferromagnet in simple cubic lattices with linear sizes $L\leq 60$. This system is widely recognized as an appropriate model for the magnetic properties of RbMnF$_3$. Time-evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using a new algorithm implemented by Krech {\it etal}, which is based on fourth-order Suzuki-Trotter decompositions of exponential operators. The dynamic structure factor was calculated from the space- and time-displaced spin-spin correlation function. The crossover from hydrodynamic to critical behavior of the dispersion curve and spin-wave half-width was studied as the temperature was increased towards the critical temperature. The dynamic critical exponent was estimated to be $z=(1.43\pm 0.03)$, which is slightly lower than the dynamic scaling prediction, but in good agreement with a recent experimental value. Direct, quantitative comparisons of both the dispersion curve and the lineshapes obtained from our simulations with very recent experimental results for RbMnF$_3$ are presented.Comment: 30 pages, RevTex, 9 figures, to appear in PR

The path-coalescence transition and its applications

We analyse the motion of a system of particles subjected a random force fluctuating in both space and time, and experiencing viscous damping. When the damping exceeds a certain threshold, the system undergoes a phase transition: the particle trajectories coalesce. We analyse this transition by mapping it to a Kramers problem which we solve exactly. In the limit of weak random force we characterise the dynamics by computing the rate at which caustics are crossed, and the statistics of the particle density in the coalescing phase. Last but not least we describe possible realisations of the effect, ranging from trajectories of raindrops on glass surfaces to animal migration patterns.Comment: 4 pages, 3 figures; revised version, as publishe

Topological orders and Edge excitations in FQH states

Fractional quantum Hall (FQH) liquids contain extremely rich internal structures which represent a whole new kind of ordering. We discuss characterization and classification of the new orders (which is called topological orders). We also discuss the edge excitations in FQH liquids, which form the so-called chiral Luttinger liquids. The chiral Luttinger liquids at the edges also have very rich structures as a reflection of the rich topological orders in the bulk. Thus, edge excitations provide us a practical way to measure topological orders in experiments.Comment: 67 pages, plain-tex, 3 figures. The section about spin vector was rewritten to make it more readabl

Contacts and Edge State Equilibration in the Fractional Quantum Hall Effect

We develop a simple kinetic equation description of edge state dynamics in the fractional quantum Hall effect (FQHE), which allows us to examine in detail equilibration processes between multiple edge modes. As in the integer quantum Hall effect (IQHE), inter-mode equilibration is a prerequisite for quantization of the Hall conductance. Two sources for such equilibration are considered: Edge impurity scattering and equilibration by the electrical contacts. Several specific models for electrical contacts are introduced and analyzed. For FQHE states in which edge channels move in both directions, such as $\nu=2/3$, these models for the electrical contacts {\it do not} equilibrate the edge modes, resulting in a non-quantized Hall conductance, even in a four-terminal measurement. Inclusion of edge-impurity scattering, which {\it directly} transfers charge between channels, is shown to restore the four-terminal quantized conductance. For specific filling factors, notably $\nu =4/5$ and $\nu=4/3$, the equilibration length due to impurity scattering diverges in the zero temperature limit, which should lead to a breakdown of quantization for small samples at low temperatures. Experimental implications are discussed.Comment: 14 pages REVTeX, 6 postscript figures (uuencoded and compressed

Tunneling gap of laterally separated quantum Hall states

We use a method of matched asymptotics to determine the energy gap of two counter-propagating, strongly interacting, quantum Hall edge states. The microscopic edge state dispersion and Coulomb interactions are used to precisely constrain the short-distance behavior of an integrable field theory, which then determines the low energy spectrum. We discuss the relationship of our results to the tunneling measurements of Kang et al., Nature 403, 59 (2000).Comment: 4 pages, 1 figur

Quantized Thermal Transport in the Fractional Quantum Hall Effect

We analyze thermal transport in the fractional quantum Hall effect (FQHE), employing a Luttinger liquid model of edge states. Impurity mediated inter-channel scattering events are incorporated in a hydrodynamic description of heat and charge transport. The thermal Hall conductance, $K_H$, is shown to provide a new and universal characterization of the FQHE state, and reveals non-trivial information about the edge structure. The Lorenz ratio between thermal and electrical Hall conductances {\it violates} the free-electron Wiedemann-Franz law, and for some fractional states is predicted to be {\it negative}. We argue that thermal transport may provide a unique way to detect the presence of the elusive upstream propagating modes, predicted for fractions such as $\nu=2/3$ and $\nu=3/5$.Comment: 6 pages REVTeX, 2 postscript figures (uuencoded and compressed