Gap Filling as Exact Path Length Problem

Peer reviewe

Fermionic Chern-Simons theory for the Fractional Quantum Hall Effect in Bilayers

We generalize the fermion Chern-Simons theory for the Fractional Hall Effect (FQHE) which we developed before, to the case of bilayer systems. We study the complete dynamic response of these systems and predict the experimentally accessible optical properties. In general, for the so called $(m, m, n)$ states, we find that the spectrum of collective excitations has a gap, and the wave function has the Jastrow-Slater form, with the exponents determined by the coefficients $m$, and $n$. We also find that the $(m,m,m)$ states, {\it i.~e.~}, those states whose filling fraction is $1\over m$, have a gapless mode which may be related with the spontaneous appearance of the interlayer coherence. Our results also indicate that the gapless mode makes a contribution to the wave function of the $(m,m,m)$ states analogous to the phonon contribution to the wave function of superfluid $\rm{He}_4$. We calculate the Hall conductance, and the charge and statistics of the quasiparticles. We also present an $SU(2)$ generalization of this theory relevant to spin unpolarized or partially polarized single layers.Comment: 55 pages, Urbana Prepin

Geometric frustration and magnetization plateaus in quantum spin and Bose-Hubbard models on tubes

We study XXZ Heisenberg models on frustrated triangular lattices wrapped around a cylinder. In addition to having interesting magnetic phases, these models are equivalent to Bose-Hubbard models that describe the physical problem of adsorption of noble gases on the surface of carbon nanotubes. We find analytical results for the possible magnetization plateau values as a function of the wrapping vectors of the cylinder, which in general introduce extra geometric frustration besides the one due to the underlying triangular lattice. We show that for particular wrapping vectors $(N,0)$, which correspond to the zig-zag nanotubes, there is a macroscopically degenerate ground state in the classical Ising limit. The Hilbert space for the degenerate states can be enumerated by a mapping first into a path in a square lattice wrapped around a cylinder (a Bratteli diagram), and then to free fermions interacting with a single ${\bf Z}_N$ degree of freedom. From this model we obtain the spectrum in the anisotropic Heisenberg limit, showing that it is gapless. The continuum limit is a $c=1$ conformal field theory with compactification radius $R=N$ set by the physical tube radius. We show that the compactification radius quantization is exact in the projective $J_\perp/J_z \ll 1$ limit, and that higher order corrections reduce the value of $R$. The particular case of a $(N=2,0)$ tube, which corresponds to a 2-leg ladder with cross links, is studied separately and shown to be gapped because the fermion mapped problem contains superconducting pairing terms.Comment: 10 pages, 11 figure

Link between the hierarchy of fractional quantum Hall states and Haldane's conjecture for quantum spin chains

We study a strong coupling expansion of the $\nu=1/3$ fractional quantum Hall state away from the Tao-Thouless limit and show that the leading quantum fluctuations lead to an effective spin-1 Hamiltonian that lacks parity symmetry. By analyzing the energetics, discrete symmetries of low-lying excitations, and string order parameters, we demonstrate that the $\nu=1/3$ fractional quantum Hall state is adiabatically connected to both Haldane and large-$D$ phases, and is characterized by a string order parameter which is dual to the ordinary one. This result indicates a close relation between (a generalized form of) the Haldane conjecture for spin chains and the fractional quantum Hall effect.Comment: 8 pages, 9 figure

3D wedge filling and 2D random-bond wetting

Fluids adsorbed in 3D wedges are shown to exhibit two types of continuous interfacial unbinding corresponding to critical and tricritical filling respectively. Analytic solution of an effective interfacial model based on the transfer-matrix formalism allows us to obtain the asymptotic probability distribution functions for the interfacial height when criticality and tricriticality are approached. Generalised random walk arguments show that, for systems with short-ranged forces, the critical singularities at these transitions are related to 2D complete and critical wetting with random bond disorder respectively.Comment: 7 pages, 3 figures, accepted for publication in Europhysics Letter

Equilibrium Current and Orbital Magnetization in a Quantum Hall Fluid

We present a general theory for the equilibrium current distribution in an interacting two-dimensional electron gas subjected to a perpendicular magnetic field, and confined by a potential that varies slowly on the scale of the magnetic length. The distribution is found to consist of strips or channels of current, which alternate in direction, and which have universal integrated strength.Comment: 13 pages, Revtex, to appear in the proceedings of the "Workshop on Novel Physics in Low-Dimensional Electron Systems" held in Madra

Spin-Charge Separation in the t−Jt-J Model: Magnetic and Transport Anomalies

A real spin-charge separation scheme is found based on a saddle-point state of the $t-J$ model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed-point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at {\em finite doping} so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic {\em residual} couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at ($\pi/a$, $\pi/a$) with a doping-dependent width ($\propto \sqrt{\delta}$, $\delta$ is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exits a characteristic temperature scale below which a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a {\em finite} energy regime. In transport, a strong short-range phase interference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-$T$ resistivity and $T^2$ Hall-angle. We discuss the striking similarities of these theoretical features with those found in the high-$T_c$ cuprates and give aComment: 70 pages, RevTex, hard copies of 7 figures available upon request; minor revisions in the text and references have been made; To be published in July 1 issue of Phys. Rev. B52, (1995

(Mis-)handling gauge invariance in the theory of the quantum Hall effect III: The instanton vacuum and chiral edge physics

The concepts of an instanton vacuum and F-invariance are used to derive a complete effective theory of massless edge excitations in the quantum Hall effect. We establish, for the first time, the fundamental relation between the instanton vacuum approach and the theory of chiral edge bosons. Two longstanding problems of smooth disorder and Coulomb interactions are addressed. We introduce a two dimensional network of chiral edge states and tunneling centers (saddlepoints) as a model for the plateau transitions. We derive a mean field theory including the Coulomb interactions and explain the recent empirical fits to transport at low temperatures. Secondly, we address the problem of electron tunneling into the quantum Hall edge. We express the problem in terms of an effective Luttinger liquid with conductance parameter (g) equal to the filling fraction (\nu) of the Landau band. Hence, even in the integral regime our results for tunneling are completely non-Fermi liquid like, in sharp contrast to the predictions of single edge theories.Comment: 51 pages, 8 figures; section IIA3 completely revised, section IIB and appendix C corrected; submitted to Phys.Rev.