Laughlin State on Stretched and Squeezed Cylinders and Edge Excitations in Quantum Hall Effect

We study the Laughlin wave function on the cylinder. We find it only describes an incompressible fluid when the two lengths of the cylinder are comparable. As the radius is made smaller at fixed area, we observe a continuous transition to the charge density wave Tao-Thouless state. We also present some exact properties of the wave function in its polynomial form. We then study the edge excitations of the quantum Hall incompressible fluid modeled by the Laughlin wave function. The exponent describing the fluctuation of the edge predicted by recent theories is shown to be identical with numerical calculations. In particular, for $\nu=1/3$, we obtain the occupation amplitudes of edge state $n(k)$ for 4-10 electron size systems. When plotted as a function of the scaled wave vector they become essentially free of finite-size effects. The resulting curve obtains a very good agreement with the appropriate infinite-size Calogero-Sutherland model occupation numbers. Finally, we numerically obtain $n(k)$ of the edge excitations for some pairing states which may be relevant to the $\nu=5/2$ incompressible Hall state.Comment: 25 pages revtex, 9 uuencoded figures, submitted separately, also available from first author. CSULA-94-1

Quantum Chemistry, Anomalous Dimensions, and the Breakdown of Fermi Liquid Theory in Strongly Correlated Systems

We formulate a local picture of strongly correlated systems as a Feynman sum over atomic configurations. The hopping amplitudes between these atomic configurations are identified as the renormalization group charges, which describe the local physics at different energy scales. For a metallic system away from half-filling, the fixed point local Hamiltonian is a generalized Anderson impurity model in the mixed valence regime. There are three types of fixed points: a coherent Fermi liquid (FL) and two classes of self-similar (scale invariant) phases which we denote incoherent metallic states (IMS). When the transitions between the atomic configurations proceed coherently at low energies, the system is a Fermi liquid. Incoherent transitions between the low energy atomic configurations characterize the incoherent metallic states. The initial conditions for the renormalization group flow are determined by the physics at rather high energy scales. This is the domain of local quantum chemistry. We use simple quantum chemistry estimates to specify the basin of attraction of the IMS fixed points.Comment: 12 pages, REVTE

Coordinate Representation of the Two-Spinon wavefunction and Spinon Interaction

By deriving and studying the coordinate representation for the two-spinon wavefunction, we show that spinon excitations in the Haldane-Shastry model interact. The interaction is given by a short-range attraction and causes a resonant enhancement in the two-spinon wavefunction at short separations between the spinons. We express the spin susceptibility for a finite lattice in terms of the resonant enhancement, given by the two-spinon wavefunction at zero separation. In the thermodynamic limit, the spinon attraction turns into the square-root divergence in the dynamical spin susceptibility.Comment: 19 pages, 5 .eps figure

Breakdown of Luttinger liquid state in one-dimensional frustrated spinless fermion model

Haldane hypothesis about the universality of Luttinger liquid (LL) behavior in conducting one-dimensional (1D) fermion systems is checked numerically for spinless fermion model with next-nearest-neighbor interactions. It is shown that for large enough interactions the ground state can be gapless (metallic) due to frustrations but not be LL. The exponents of correlation functions for this unusual conducting state are found numerically by finite-size method.Comment: 3 pages, 4 figures, RevTe

Exact calculation of the ground-state dynamical spin correlation function of a S=1/2 antiferromagnetic Heisenberg chain with free spinons

We calculate the exact dynamical magnetic structure factor S(Q,E) in the ground state of a one-dimensional S=1/2 antiferromagnet with gapless free S=1/2 spinon excitations, the Haldane-Shastry model with inverse-square exchange, which is in the same low-energy universality class as Bethe's nearest-neighbor exchange model. Only two-spinon excited states contribute, and S(Q,E) is found to be a very simple integral over these states.Comment: 11 pages, LaTeX, RevTeX 3.0, cond-mat/930903

Yangian-invariant field theory of matrix-vector models

We extend our study of the field-theoretic description of matrix-vector models and the associated many-body problems of one dimensional particles with spin. We construct their Yangian-su(R) invariant Hamiltonian. It describes an interacting theory of a c=1 collective boson and a k=1 su(R) current algebra. When $R \geq 3$ cubic-current terms arise. Their coupling is determined by the requirement of the Yangian symmetry. The Hamiltonian can be consistently reduced to finite-dimensional subspaces of states, enabling an explicit computation of the spectrum which we illustrate in the simplest case.Comment: Extensive modifications in the construction of the spinon basis and the subsequent computations of eigenvalues and eigenvectors. Title and references modified. To appear in Nuclear Physics B. 21 pages, Late

The effect of host heterogeneity and parasite intragenomic interactions on parasite population structure

Understanding the processes that shape the genetic structure of parasite populations and the functional consequences of different parasite genotypes is critical for our ability to predict how an infection can spread through a host population and for the design of effective vaccines to combat infection and disease. Here, we examine how the genetic structure of parasite populations responds to host genetic heterogeneity. We consider the well-characterized molecular specificity of major histocompatibility complex binding of antigenic peptides to derive deterministic and stochastic models. We use these models to ask, firstly, what conditions favour the evolution of generalist parasite genotypes versus specialist parasite genotypes? Secondly, can parasite genotypes coexist in a population? We find that intragenomic interactions between parasite loci encoding antigenic peptides are pivotal in determining the outcome of evolution. Where parasite loci interact synergistically (i.e. the recognition of additional antigenic peptides has a disproportionately large effect on parasite fitness), generalist parasite genotypes are favoured. Where parasite loci act multiplicatively (have independent effects on fitness) or antagonistically (have diminishing effects on parasite fitness), specialist parasite genotypes are favoured. A key finding is that polymorphism is not stable and that, with respect to functionally important antigenic peptides, parasite populations are dominated by a single genotype

Exact Dynamical Correlation Functions of Calogero-Sutherland Model and One-Dimensional Fractional Statistics

One-dimensional model of non-relativistic particles with inverse-square interaction potential known as Calogero-Sutherland Model (CSM) is shown to possess fractional statistics. Using the theory of Jack symmetric polynomial the exact dynamical density-density correlation function and the one-particle Green's function (hole propagator) at any rational interaction coupling constant $\lambda = p/q$ are obtained and used to show clear evidences of the fractional statistics. Motifs representing the eigenstates of the model are also constructed and used to reveal the fractional {\it exclusion} statistics (in the sense of Haldane's ``Generalized Pauli Exclusion Principle''). This model is also endowed with a natural {\it exchange } statistics (1D analog of 2D braiding statistics) compatible with the {\it exclusion} statistics. (Submitted to PRL on April 18, 1994)Comment: Revtex 11 pages, IASSNS-HEP-94/27 (April 18, 1994

Challenges and opportunities surrounding Catholic education

Catholic education faces a number of serious challenges including cultural and political disrespect for, and hostility towards religion in general and Catholicism in particular, and lack of knowledge of, and commitment to, Catholic beliefs and values among Catholic educational administrators, school managers, teachers, and other staff, as well as the diminishing percentage of even nominally Catholic staff. I set these matters within the context of broader challenges surrounding Catholic education, deriving from three cultural movements: the reformation, the emergence of liberalism, and the scientific revolution, which undermined the synthesis of scripture, theology, and speculative and practical philosophy achieved in the high middle-ages. I propose in response a creative critique showing that what is of authentic value in modernity can be accommodated within the traditional synthesis. I also connect that tradition with strands of eastern philosophy suggesting that the movement of people, ideas, and traditions from Eastern cultures into historically Western societies provides an opportunity for further synthesis of a wisdom-based approach to education.Peer reviewe

Renormalization-group study of a magnetic impurity in a Luttinger liquid

A generalized Anderson model for a magnetic impurity in an interacting one-dimensional electron gas is studied via a mapping onto a classical Coulomb gas. For weak potential scattering, the local-moment parameter regime expands as repulsive bulk interactions become stronger, but the Kondo scale for the quenching of the impurity moment varies nonmonotonically. There also exist two regimes dominated by backward potential scattering: one in which the impurity is nonmagnetic, and another in which an unquenched local moment survives down to very low temperatures.Comment: REVTeX, 4 pages, 3 epsf-embedded EPS figure