Anomalous tunneling conductances of a spin singlet \nu=2/3 edge states: Interplay of Zeeman splitting and Long Range Coulomb Interaction

The point contact tunneling conductance between edges of the spin singlet $\nu=2/3,\hat{K}=(3/3/0)$ quantum Hall states is studied both in the quasiparticle tunneling picture and in the electron tunneling picture. Due to the interplay of Zeeman splitting and the long range Coulomb interaction between edges of opposite chirality novel spin excitations emerge, and their effect is characterized by anomalous exponents of the charge and spin tunneling conductances in various temperature ranges. Depending on the kinds of scatterings at the point contact and the tunneling mechanism the anomalous interaction in spin sector may enhance or suppress the tunneling conductances. The effects of novel spin excitation are also relevant to the recent NMR experiments on quantum Hall edges.Comment: Revtex File, 7 pages: To be published in Physical Reviews

Anomalous Exponent of the Spin Correlation Function of a Quantum Hall Edge

The charge and spin correlation functions of partially spin-polarized edge electrons of a quantum Hall bar are studied using effective Hamiltonian and bosonization techniques. In the presence of the Coulomb interaction between the edges with opposite chirality we find a different crossover behavior in spin and charge correlation functions. The crossover of the spin correlation function in the Coulomb dominated regime is characterized by an anomalous exponent, which originates from the finite value of the effective interaction for the spin degree of freedom in the long wavelength limit. The anomalous exponent may be determined by measuring nuclear spin relaxation rates in a narrow quantum Hall bar or in a quantum wire in strong magnetic fields.Comment: 4 pages, Revtex file, no figures. To appear in Physical Revews B, Rapid communication

From the Chern-Simons theory for the fractional quantum Hall effect to the Luttinger model of its edges

The chiral Luttinger model for the edges of the fractional quantum Hall effect is obtained as the low energy limit of the Chern-Simons theory for the two dimensional system. In particular we recover the Kac-Moody algebra for the creation and annihilation operators of the edge density waves and the bosonization formula for the electronic operator at the edge.Comment: 4 pages, LaTeX, 1 Postscript figure include

Quantum Orders and Symmetric Spin Liquids

A concept -- quantum order -- is introduced to describe a new kind of orders that generally appear in quantum states at zero temperature. Quantum orders that characterize universality classes of quantum states (described by {\em complex} ground state wave-functions) is much richer then classical orders that characterize universality classes of finite temperature classical states (described by {\em positive} probability distribution functions). The Landau's theory for orders and phase transitions does not apply to quantum orders since they cannot be described by broken symmetries and the associated order parameters. We find projective representations of symmetry groups (which will be called projective symmetry groups) can be used to characterize quantum orders. With the help of quantum orders and the projective symmetry groups, we construct hundreds of symmetric spin liquids, which have SU(2), U(1) or $Z_2$ gauge structures at low energies. Remarkably, some of the stable quantum phases support gapless excitations even without any spontaneous symmetry breaking. We propose that it is the quantum orders (instead of symmetries) that protect the gapless excitations and make algebraic spin liquids and Fermi spin liquids stable. Since high $T_c$ superconductors are likely to be described by a gapless spin liquid, the quantum orders and their projective symmetry group descriptions lay the foundation for spin liquid approach to high $T_c$ superconductors.Comment: 58 pages, RevTeX4 home page: http://dao.mit.edu/~we

The Unusual Superconducting State of Underdoped Cuprates

There is increasing experimental evidence that the superconducting energy gap $\Delta_0$ in the underdoped cuprates is independent of doping concentration $x$ while the superfluid density is linear in $x$. We show that under these conditions, thermal excitation of the quasiparticles is very effective in destroying the superconducting state, so that $T_c$ is proportional to $x\Delta_0$ and part of the gap structure remains in the normal state. We then estimate $H_{c2}$ and predict it to be proportional to $x^2$. We also discuss to what extent the assumptions that go into the quasiparticle description can be derived in the U(1) and SU(2) formulations of the t-J model.Comment: 4 pages RevTe

On the Conductance Sum Rule for the Hierarchical Edge States of the Fractional Quantum Hall Effect

The conductance sum rule for the hierarchical edge channel currents of a Fractional Quantum Hall Effect state is derived analytically within the Haldane-Halperin hierarchy scheme. We provide also an intuitive interpretation for the hierarchical drift velocities of the edge excitations.Comment: 11 pages, no figure, Revtex 3.0, IC/93/329, ASITP-93-5

The edge state network model and the global phase diagram

The effects of randomness are investigated in the fractional quantum Hall systems. Based on the Chern-Simons Ginzburg-Landou theory and considering relevant quasi-particle tunneling, the edge state network model for the hierarchical state is introduced and the plateau-plateau transition and liquid-insulator transition are discussed. This model has duality which corresponds to the relation of the quantum Hall liquid phase and the Hall insulating phase and reveals a mechanism in the weak coupling regime.Comment: 5 page RevTe

On the Electromagnetic Response of Charged Bosons Coupled to a Chern-Simons Gauge Field: A Path Integral Approach

We analyze the electromagnetic response of a system of charged bosons coupled to a Chern-Simons gauge field. Path integral techniques are used to obtain an effective action for the particle density of the system dressed with quantum fluctuations of the CS gauge field. From the action thus obtained we compute the U(1) current of the theory for an arbitrary electromagnetic external field. For the particular case of a homogeneous external magnetic field, we show that the quantization of the transverse conductivity is exact, even in the presence of an arbitrary impurity distribution. The relevance of edge states in this context is analyzed. The propagator of density fluctuations is computed, and an effective action for the matter density in the presence of a vortex excitation is suggested.Comment: LaTex file, 27 pages, no figure

Aharonov-Bohm effect in the chiral Luttinger liquid

Edge states of the quantum Hall fluid provide an almost unparalled opportunity to study mesoscopic effects in a highly correlated electron system. In this paper we develop a bosonization formalism for the finite-size edge state, as described by chiral Luttinger liquid theory, and use it to study the Aharonov-Bohm effect. The problem we address may be realized experimentally by measuring the tunneling current between two edge states through a third edge state formed around an antidot in the fractional quantum Hall effect regime. A renormalization group analysis reveals the existence of a two-parameter universal scaling function G(X,Y) that describes the Aharonov-Bohm resonances. We also show that the strong renormalization of the tunneling amplitudes that couple the antidot to the incident edge states, together with the nature of the Aharonov-Bohm interference process in a chiral system, prevent the occurrence of perfect resonances as the magnetic field is varied, even at zero temperature.Comment: 16 pages, Revtex, 5 figures available from [email protected]

An SU(2) Formulation of the t-J model: Application to Underdoped Cuprates

We develop a slave-boson theory for the t-J model at finite doping which respect a SU(2) symmetry -- a symmetry previously known to be important at half filling. The mean field phase diagram is found to be consistent with the phases observed in the cuprate superconductors, which contains d-wave superconductor, spin gap, strange metal, and Fermi liquid phases. The spin gap phase is best understood as the staggered flux phase, which is nevertheless translationally invariant for physical quantities. The physical electron spectral function shows small Fermi segments at low doping which continuously evolve into the large Fermi surface at high doping concentrations. The close relation between the SU(2) and the U(1) slave-boson theory is discussed. The low energy effective theory for the low lying fluctuations is derived, and new lying modes (which were over looked in the U(1) theory) are identified.Comment: 28 pages, 8 figures, RevTe