Spectrum and Thermodynamics of the one-dimensional supersymmetric t-J model with 1/r21/r^2 exchange and hopping

We derive the spectrum and the thermodynamics of the one-dimensional supersymmetric t-J model with long range hopping and spin exchange using a set of maximal-spin eigenstates. This spectrum confirms the recent conjecture that the asymptotic Bethe-ansatz spectrum is exact. By empirical determining the spinon degeneracies of each state, we are able to explicitly construct the free energy.Comment: 13 pages, Latex, (published in PRB46, 6639 (1992)

Rectified voltage induced by a microwave field in a confined two-dimensional electron gas with a mesoscopic static vortex

We investigate the effect of a microwave field on a confined two dimensional electron gas which contains an insulating region comparable to the Fermi wavelength. The insulating region causes the electron wave function to vanish in that region. We describe the insulating region as a static vortex. The vortex carries a flux which is determined by vanishing of the charge density of the electronic fluid due to the insulating region. The sign of the vorticity for a hole is opposite to the vorticity for adding additional electrons. The vorticity gives rise to non-commuting kinetic momenta. The two dimensional electron gas is described as fluid with a density which obeys the Fermi-Dirac statistics. The presence of the confinement potential gives rise to vanishing kinetic momenta in the vicinity of the classical turning points. As a result, the Cartesian coordinate do not commute and gives rise to a Hall current which in the presence of a modified Fermi-Surface caused by the microwave field results in a rectified voltage. Using a Bosonized formulation of the two dimensional gas in the presence of insulating regions allows us to compute the rectified current. The proposed theory may explain the experimental results recently reported by J. Zhang et al.Comment: 14 pages, 2 figure

Fractional quantum Hall effect in the absence of Landau levels

It has been well-known that topological phenomena with fractional excitations, i.e., the fractional quantum Hall effect (FQHE) \cite{Tsui1982} will emerge when electrons move in Landau levels. In this letter, we report the discovery of the FQHE in the absence of Landau levels in an interacting fermion model. The non-interacting part of our Hamiltonian is the recently proposed topologically nontrivial flat band model on the checkerboard lattice \cite{sun}. In the presence of nearest-neighboring repulsion ($U$), we find that at 1/3 filling, the Fermi-liquid state is unstable towards FQHE. At 1/5 filling, however, a next-nearest-neighboring repulsion is needed for the occurrence of the 1/5 FQHE when $U$ is not too strong. We demonstrate the characteristic features of these novel states and determine the phase diagram correspondingly.Comment: 6 pages and 4 figure

The Magic Angle "Mystery" in Electron Energy Loss Spectroscopy: Relativistic and Dielectric Corrections

Recently it has been demonstrated that a careful treatment of both longitudinal and transverse matrix elements in electron energy loss spectra can explain the mystery of relativistic effects on the {\it magic angle}. Here we show that there is an additional correction of order $(Z\alpha)^2$ where $Z$ is the atomic number and $\alpha$ the fine structure constant, which is not necessarily small for heavy elements. Moreover, we suggest that macroscopic electrodynamic effects can give further corrections which can break the sample-independence of the magic angle.Comment: 10 pages (double column), 6 figure

Jammed Disks of Two Sizes in a Narrow Channel

A granular-matter model is exactly solved, where disks of two sizes and weights in alternating sequence are confined to a narrow channel. The axis of the channel is horizontal and its plane vertical. Disk sizes and channel width are such that under jamming no disks remain loose and all disks touch one wall. Jammed microstates are characterized via statistically interacting particles constructed out of two-disk tiles. Jammed macrostates depend on measures of expansion work, gravitational potential energy, and intensity of random agitations before jamming. The dependence of configurational entropy on excess volume exhibits a critical point

Spinons and triplons in spatially anisotropic frustrated antiferromagnets

The search for elementary excitations with fractional quantum numbers is a central challenge in modern condensed matter physics. We explore the possibility in a realistic model for several materials, the spin-1/2 spatially anisotropic frustrated Heisenberg antiferromagnet in two dimensions. By restricting the Hilbert space to that expressed by exact eigenstates of the Heisenberg chain, we derive an effective Schr\"odinger equation valid in the weak interchain-coupling regime. The dynamical spin correlations from this approach agree quantitatively with inelastic neutron measurements on the triangular antiferromagnet Cs_2CuCl_4. The spectral features in such antiferromagnets can be attributed to two types of excitations: descendents of one-dimensional spinons of individual chains, and coherently propagating "triplon" bound states of spinon pairs. We argue that triplons are generic features of spatially anisotropic frustrated antiferromagnets, and arise because the bound spinon pair lowers its kinetic energy by propagating between chains.Comment: 16 pages, 6 figure

From Luttinger to Fermi liquids in organic conductors

This chapter reviews the effects of interactions in quasi-one dimensional systems, such as the Bechgaard and Fabre salts, and in particular the Luttinger liquid physics. It discusses in details how transport measurements both d.c. and a.c. allow to probe such a physics. It also examine the dimensional crossover and deconfinement transition occurring between the one dimensional case and the higher dimensional one resulting from the hopping of electrons between chains in the quasi-one dimensional structure.Comment: To be published In the book "The Physics of Organic Conductors and Superconductors", Springer, 2007, ed. A. Lebe

Unconventional quantum Hall effect and Berry’s phase 2pi in bilayer graphene.

There are known two distinct types of the integer quantum Hall effect. One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems, and the other is its relativistic counterpart recently observed in graphene, where charge carriers mimic Dirac fermions characterized by Berry’s phase pi, which results in a shifted positions of Hall plateaus. Here we report a third type of the integer quantum Hall effect. Charge carriers in bilayer graphene have a parabolic energy spectrum but are chiral and exhibit Berry’s phase 2pi affecting their quantum dynamics. The Landau quantization of these fermions results in plateaus in Hall conductivity at standard integer positions but the last (zero-level) plateau is missing. The zero-level anomaly is accompanied by metallic conductivity in the limit of low concentrations and high magnetic fields, in stark contrast to the conventional, insulating behavior in this regime. The revealed chiral fermions have no known analogues and present an intriguing case for quantum-mechanical studies

Generalized N = 2 Super Landau Models

We generalize previous results for the superplane Landau model to exhibit an explicit worldline N = 2 supersymmetry for an arbitrary magnetic field on any two-dimensional manifold. Starting from an off-shell N = 2 superfield formalism, we discuss the quantization procedure in the general case characterized by two independent potentials on the manifold and show that the relevant Hamiltonians are factorizable. In the restricted case when both the Gauss curvature and the magnetic field are constant over the manifold and, as a consequence, the underlying potentials are related, the Hamiltonians admit infinite series of factorization chains implying the integrability of the associated systems. We explicitly determine the spectrum and eigenvectors for the particular model with CP^1 as the bosonic manifold.Comment: 26 page

Observation of unidirectional backscattering-immune topological electromagnetic states

One of the most striking phenomena in condensed-matter physics is the quantum Hall effect, which arises in two-dimensional electron systems subject to a large magnetic field applied perpendicular to the plane in which the electrons reside. In such circumstances, current is carried by electrons along the edges of the system, in so-called chiral edge states (CESs). These are states that, as a consequence of nontrivial topological properties of the bulk electronic band structure, have a unique directionality and are robust against scattering from disorder. Recently, it was theoretically predicted that electromagnetic analogues of such electronic edge states could be observed in photonic crystals, which are materials having refractive-index variations with a periodicity comparable to the wavelength of the light passing through them. Here we report the experimental realization and observation of such electromagnetic CESs in a magneto-optical photonic crystal fabricated in the microwave regime. We demonstrate that, like their electronic counterparts, electromagnetic CESs can travel in only one direction and are very robust against scattering from disorder; we find that even large metallic scatterers placed in the path of the propagating edge modes do not induce reflections. These modes may enable the production of new classes of electromagnetic device and experiments that would be impossible using conventional reciprocal photonic states alone. Furthermore, our experimental demonstration and study of photonic CESs provides strong support for the generalization and application of topological band theories to classical and bosonic systems, and may lead to the realization and observation of topological phenomena in a generally much more controlled and customizable fashion than is typically possible with electronic systems