Antiferromagnetism in the Exact Ground State of the Half Filled Hubbard Model on the Complete-Bipartite Graph

As a prototype model of antiferromagnetism, we propose a repulsive Hubbard Hamiltonian defined on a graph \L={\cal A}\cup{\cal B} with ${\cal A}\cap {\cal B}=\emptyset$ and bonds connecting any element of ${\cal A}$ with all the elements of ${\cal B}$. Since all the hopping matrix elements associated with each bond are equal, the model is invariant under an arbitrary permutation of the ${\cal A}$-sites and/or of the ${\cal B}$-sites. This is the Hubbard model defined on the so called $(N_{A},N_{B})$-complete-bipartite graph, $N_{A}$ ($N_{B}$) being the number of elements in ${\cal A}$ (${\cal B}$). In this paper we analytically find the {\it exact} ground state for $N_{A}=N_{B}=N$ at half filling for any $N$; the repulsion has a maximum at a critical $N$-dependent value of the on-site Hubbard $U$. The wave function and the energy of the unique, singlet ground state assume a particularly elegant form for N \ra \inf. We also calculate the spin-spin correlation function and show that the ground state exhibits an antiferromagnetic order for any non-zero $U$ even in the thermodynamic limit. We are aware of no previous explicit analytic example of an antiferromagnetic ground state in a Hubbard-like model of itinerant electrons. The kinetic term induces non-trivial correlations among the particles and an antiparallel spin configuration in the two sublattices comes to be energetically favoured at zero Temperature. On the other hand, if the thermodynamic limit is taken and then zero Temperature is approached, a paramagnetic behavior results. The thermodynamic limit does not commute with the zero-Temperature limit, and this fact can be made explicit by the analytic solutions.Comment: 19 pages, 5 figures .ep

Some exact results for the multicomponent t-J model

We present a generalization of the Sutherland's multicomponent model. Our extension includes both the ferromagnetic and the antiferromagnetic t-J model for any value of the exchange coupling J and the hopping parameter t. We prove rigorously that for one dimensional chains the ground-state of the generalized model is non-degenerate. As a consequence, the ordering of energy levels of the antiferromagnetic t-J model is determined. Our result rigorously proves and extends the analysis carried out by Sutherland in establishing the phase diagram of the model as a function of the number of components.Comment: 11 pages, RevTeX 3.0, no figure

Skyrmions in Higher Landau Levels

We calculate the energies of quasiparticles with large numbers of reversed spins (``skyrmions'') for odd integer filling factors 2k+1, k is greater than or equals 1. We find, in contrast with the known result for filling factor equals 1 (k = 0), that these quasiparticles always have higher energy than the fully polarized ones and hence are not the low energy charged excitations, even at small Zeeman energies. It follows that skyrmions are the relevant quasiparticles only at filling factors 1, 1/3 and 1/5.Comment: 10 pages, RevTe

Opial-Type Integral Inequalities Involving Several Arbitrary Increasing Convex Functions

AbstractSome new Opial-type integral inequalities involving several arbitrary increasing convex functions on both sides are proved. These results generalise and yield important complementary results of some known integral inequalities established by G. I. Rozanova, B. G. Pachpatte, E. K. Godunova and V. I. Levin, and T. S. Hwang and G. S. Yang

Thermodynamical Bethe Ansatz and Condensed Matter

The basics of the thermodynamic Bethe ansatz equation are given. The simplest case is repulsive delta function bosons, the thermodynamic equation contains only one unknown function. We also treat the XXX model with spin 1/2 and the XXZ model and the XYZ model. This method is very useful for the investigation of the low temperature thermodynamics of solvable systems.Comment: 52 pages, 6 figures, latex, lamuphys.st

REMOVED: Optimization of VMD Process as Draw Solution Recovery Unit in FO Process

This article has been removed: please see Elsevier Policy on Article Withdrawal (http://www.elsevier.com/locate/withdrawalpolicy).This article has been removed at the request of the Executive Publisher.This article has been removed because it was published without the permission of the author(s)

Asymptotics of basic Bessel functions and q-Laguerre polynomials

AbstractWe establish a large n complete asymptotic expansion for q-Laguerre polynomials and a complete asymptotic expansion for a q-Bessel function of large argument. These expansions are needed in our study of an exactly solvable random transfer matrix model for disordered electronic systems. We also give a new derivation of an asymptotic formula due to Littlewood (1907)

Wave Mechanics of Two Hard Core Quantum Particles in 1-D Box

The wave mechanics of two impenetrable hard core particles in 1-D box is analyzed. Each particle in the box behaves like an independent entity represented by a {\it macro-orbital} (a kind of pair waveform). While the expectation value of their interaction, $$, vanishes for every state of two particles, the expectation value of their relative separation,$$, satisfies $\ge \lambda/2$ (or $q \ge \pi/d$, with $2d = L$ being the size of the box). The particles in their ground state define a close-packed arrangement of their wave packets (with $= \lambda/2$, phase position separation $\Delta\phi = 2\pi$ and momentum $|q_o| = \pi/d$) and experience a mutual repulsive force ({\it zero point repulsion}) $f_o = h^2/2md^3$ which also tries to expand the box. While the relative dynamics of two particles in their excited states represents usual collisional motion, the same in their ground state becomes collisionless. These results have great significance in determining the correct microscopic understanding of widely different many body systems.Comment: 12 pages, no figur

Tau-Function Constructions of the Recurrence Coefficients of Orthogonal Polynomials

AbstractIn this paper we compute the recurrence coefficients of orthogonal polynomials using τ-function techniques. It is shown that for polynomials orthogonal with respect to positive weight functions on a noncompact interval, the recurrence coefficient can be expressed as the change in the chemical potential which, for sufficiently largeNis the second derivative of the free energy with respect toN, the particle number. We give three examples using this technique: Freud weights, Erdős weights, and weak exponential weights

Effects of etchants in the transfer of chemical vapor deposited graphene

The quality of graphene can be strongly modified during the transfer process following chemical vapor deposition (CVD) growth. Here, we transferred CVD-grown graphene from a copper foil to a SiO2/Si substrate using wet etching with four different etchants: HNO3, FeCl3, (NH4)2S2O8, and a commercial copper etchant. We then compared the quality of graphene after the transfer process in terms of surface modifications, pollutions (residues and contaminations), and electrical properties (mobility and density). Our tests and analyses showed that the commercial copper etchant provides the best structural integrity, the least amount of residues, and the smallest doping carrier concentration