Universal periods in quantum Hall droplets

Using the hierarchy picture of the fractional quantum Hall effect, we study the ground-state periodicity of a finite size quantum Hall droplet in a quantum Hall fluid of a different filling factor. The droplet edge charge is periodically modulated with flux through the droplet and will lead to a periodic variation in the conductance of a nearby point contact, such as occurs in some quantum Hall interferometers. Our model is consistent with experiment and predicts that superperiods can be observed in geometries where no interfering trajectories occur. The model may also provide an experimentally feasible method of detecting elusive neutral modes and otherwise obtaining information about the microscopic edge structure in fractional quantum Hall states.     

Edge states tunneling in the fractional quantum Hall effect: integrability and transport

This is a short review of nonperturbative techniques that have been used in the past 5 years to study transport out of equilibrium in low dimensional, strongly interacting systems of condensed matter physics. These techniques include massless factorized scattering, the generalization of the Landauer Büttiker approach to integrable quaisparticles, and duality. The case of tunneling between edges in the fractional quantum Hall effect is discussed in details. To cite this article: H. Saleur, C. R. Physique 3 (2002) 685–695.     

Quantum Hall effect in higher dimensions

Following recent work on the quantum Hall effect on S⁴, we solve the Landau problem on the complex projective spaces $\text{C}\text{P}{}^{\mathrm{k}}$ and discuss quantum Hall states for such spaces. Unlike the case of S⁴, a finite spatial density can be obtained with a finite number of internal states for each particle. We treat the case of $\text{C}\text{P}{}^2$ in some detail considering both Abelian and nonAbelian background fields. The wavefunctions are obtained and incompressibility of the Hall states is shown. The case of $\text{C}\text{P}{}^3$ is related to the case of S⁴.     

Multichannel Kondo models in non-Abelian quantum Hall droplets

We study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state which is spatially separated from it by an integer quantum Hall state. Near a resonance, the physics at energy scales below the level spacing of the edge states of the dot is governed by a k-channel Kondo model when the quantum Hall state is a Read-Rezayi state at filling fraction nu=2+k/(k+2) or its particle-hole conjugate at nu=2+2/(k+2). The k-channel Kondo model is channel isotropic even without fine-tuning in the former state; in the latter, it is generically channel anisotropic. In the special case of k=2, our results provide a new venue, realized in a mesoscopic context, to distinguish between the Pfaffian and anti-Pfaffian states at filling fraction nu=5/2.     

Landau-Ginzburg theories for non-abelian quantum Hall states

We construct Landau-Ginzburg effective field theories for fractional quantum Hall states - such as the Pfaffian state - which exhibit non-abelian statistics. These theories rely on a Meissner construction which increases the level of a non-abelian Chem-Simons theory while simultaneously projecting out the unwanted degrees of freedom of a concomitant enveloping abelian theory. We describe this construction in the context of a system of bosons at Landau level filling factor ν = l, where the non-abelian symmetry is a dynamically generated SU(2) continuous extension of the discrete particle-hole symmetry of the lowest Landau level. We show how the physics of quasiparticles and their non-abelian statistics arises in this Landau-Ginzburg theory. We describe its relation to edge theories - where a coset construction plays the role of the Meissner projection — and discuss extensions to other states.     

Ground states of the generalized Falicov-Kimball model in one and two dimensions

A combination of small-cluster exact-diagonalization calculations and a well-controlled approximative method is used to study the ground-state phase diagram of the spin-one-half Falicov-Kimball model extended by the spin-dependent on-site interaction between localized (f) and itinerant (d) electrons. Both the magnetic and charge ordering are analysed as functions of the spin-dependent on-site interaction (J) and the total number of itinerant (N_d) and localized (N_f) electrons at selected U (the spin-independent interaction between the f and d electrons). It is shown that the spin-dependent interaction (for N_f=L, where L is the number of lattice sites) stabilizes the fully polarized (FP) and partially polarized (PP) state, while the stability region of the non polarized (NP) phase is gradually reduced. The precisely opposite effect on the stability of FP, PP and NP phases has a reduction of N_f. Moreover, the strong coupling between the f and d-electron subsystems is found for both N_f=L as well as N_f < L.     

Exact parent Hamiltonian for the quantum Hall states in a lattice

We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wave functions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wave function is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next-nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.     

Even-odd effect in spontaneously coherent bilayer quantum Hall droplets

Using exact diagonalization in the disk geometry we predict a novel even-odd effect in the Coulomb-blockade spectra of vertically coupled double quantum dots under an external magnetic field. The even-odd effect in the tunneling conductance is a direct manifestation of spontaneous interlayer phase coherence, and is similar to the even-odd resonance in the Cooper pair box problem in mesoscopic superconducting grains. Coherent fluctuations in the number of Cooper pairs in superconductors are analogous to the fluctuations in the relative number difference between the two layers in quantum Hall droplets.     

Edge states in a two-dimensional quantum walk with disorder

We investigate the effect of spatial disorder on the edge states localized at the interface between two topologically different regions. Rotation disorder can localize the quantum walk if it is strong enough to change the topology, otherwise the edge state is protected. Nonlinear spatial disorder, dependent on the walker’s state, attracts the walk to the interface even for very large coupling, preserving the ballistic transport characteristic of the clean regime.     

Model for dissipative conductance in fractional quantum Hall states

We present a model of dissipative transport in the fractional quantum Hall regime. Our model takes account of tunneling through saddle points in the effective potential for excitations created by impurities. We predict the temperature range over which activated behavior is observed and explain why this range nearly always corresponds to around a factor two in temperature in both integer quantum Hall and fractional quantum Hall systems. We identify the ratio of the gap observed in the activated behavior and the temperature of the inflection point in the Arrhenius plot as an important diagnostic for determining the importance of tunneling in real samples.     

The generalized Maxwell-Einstein system in higher dimensions

We study some consequences of the generalized Maxwell-Einstein system in higher dimensions. This generalization is such that the Maxwell-type field constructed in an evenn-dimensional space-time preserves the conformal invariance. After dimensional reduction to four dimensions, it gives rise to scalar, electromagnetic and Kalb-Ramond fields. Specifically, we analyse here some compactification processes, including the stability of the final configuration (forn=8), and anisotropic cosmological solutions (forn=6).On leave of absence from: Departamento de Física e Química, Universidade Federal do Espírito Santo, Goiabeiras, Vitória CEP 29000, Espírito Santo, Brazil     

Spin order in paired quantum Hall states

We consider quantum Hall states at even-denominator filling fractions, especially nu=5/2, in the limit of small Zeeman energy. Assuming that a paired quantum Hall state forms, we study spin ordering and its interplay with pairing. We give numerical evidence that at nu=5/2 an incompressible ground state will exhibit spontaneous ferromagnetism. The Ginzburg-Landau (GL) theory for the spin degrees of freedom of paired Hall states is a perturbed CP2 model. We compute the coefficients in the GL theory by a BCS Stoner mean-field theory for coexisting order parameters, and show that even if repulsion is smaller than that required for a Stoner instability, ferromagnetic fluctuations can induce a partially or fully polarized superconducting state.