Green's functions on finite lattices and their connection to the infinite lattice limit

It is shown that the Green's function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of translation operator. Explicit examples are given for one- and two-dimensional lattices

Canonical representation for electrons and its application to the Hubbard model

A new representation for electrons is introduced, in which the electron operators are written in terms of a spinless fermion and the Pauli operators. This representation is canonical, invertible and constraint-free. Importantly, it simplifies the Hubbard interaction. On a bipartite lattice, the Hubbard model is reduced to a form in which the exchange interaction emerges simply by decoupling the Pauli subsystem from the spinless fermion bath. This exchange correctly reproduces the large $U$ superexchange. Also derived, for $U=\pm\infty$, is the Hamiltonian to study Nagaoka ferromagnetism. In this representation, the infinite-$U$ Hubbard problem becomes elegant and easier to handle. Interestingly, the ferromagnetism in Hubbard model is found to be related to the gauge invariance of the spinless fermions. Generalization of this representation for the multicomponent fermions, a new representation for bosons, the notion of a `soft-core' fermion, and some interesting unitary transformations are introduced and discussed in the appendices.Comment: 10+ pages, 3 Figure

Anomalous dynamics in two- and three- dimensional Heisenberg-Mattis spin glasses

We investigate the spectral and localization properties of unmagnetized Heisenberg-Mattis spin glasses, in space dimensionalities $d=2$ and 3, at T=0. We use numerical transfer-matrix methods combined with finite-size scaling to calculate Lyapunov exponents, and eigenvalue-counting theorems, coupled with Gaussian elimination algorithms, to evaluate densities of states. In $d=2$ we find that all states are localized, with the localization length diverging as $\omega^{-1}$, as energy $\omega \to 0$. Logarithmic corrections to density of states behave in accordance with theoretical predictions. In $d=3$ the density-of-states dependence on energy is the same as for spin waves in pure antiferromagnets, again in agreement with theoretical predictions, though the corresponding amplitudes differ.Comment: RevTeX4, 9 pages, 9 .eps figure

The Duty to Decide vs. The Daedalian Doctrine of Abstention

It is the thesis of this article that the growing trend in the federal courts to refuse to exercise their assigned jurisdiction violates the doctrine of the separation of powers, and that the federal judiciary\u27s excuses for refusing to perform their tasks do not pass constitutional muster. Specifically, this article will demonstrate that those excuses either do not rise to a level of constitutional concern sufficient to justify the trend or are based on a perversion of the admittedly constitutional concept of federalism, a concept affording the individual citizen a structural protection against arbitrary government in additionto the structural protection flowing from separated powers, not a concept that properly can be used to deprive the individual of federal protection. After establishing the inadequacies of the courts\u27 excuses for refusing to decide cases, this article then points to the provisions of article III and article I, section 8, clause 9, of the Constitution to show that, given Congress\u27s power to create within constitutional limits the jurisdiction of the federal judiciary, 30 and given that judiciary\u27s power to decide all cases properly arising pursuant to Congress\u27s constitutional exercise of its powers, the federal courts abrogate the separation doctrine, in effect destroying their own jurisdiction, however the practice is couched in nonjurisdictional rubric, whenever they refuse to exercise such jurisdiction by not deciding those cases which Congress has determined should be decided. In short, the federal courts have a duty to decide

Dynamic properties of a nonsuperfluid Bose liquid in the random-phase approximation

Journal ArticleThe dynamic structure factor S(k,w) of a nonideal Bose liquid is calculated within the random-phase approximation and compared with neutron scattering data by Cowley and Woods for liquid helium in the temperature range Tλ<T≤4.2°K, with the conclusion that the model is wholly inadequate. A low-frequency pole in the generalized susceptibility discussed by Mattis and Landovitz is shown to be overdamped in S(k,w)

From Effective Lagrangians, to Chiral Bags, to Skyrmions with the Large-N_c Renormalization Group

We explicitly relate effective meson-baryon Lagrangian models, chiral bags, and Skyrmions in the following way. First, effective Lagrangians are constructed in a manner consistent with an underlying large-N_c QCD. An infinite set of graphs dress the bare Yukawa couplings at *leading* order in 1/N_c, and are summed using semiclassical techniques. What emerges is a picture of the large-N_c baryon reminiscent of the chiral bag: hedgehog pions for r > 1/\Lambda patched onto bare nucleon degrees of freedom for r < 1/\Lambda, where the ``bag radius'' 1/\Lambda is the UV cutoff on the graphs. Next, a novel renormalization group (RG) is derived, in which the bare Yukawa couplings, baryon masses and hyperfine baryon mass splittings run with \Lambda. Finally, this RG flow is shown to act as a *filter* on the renormalized Lagrangian parameters: when they are fine-tuned to obey Skyrme-model relations the continuum limit \Lambda --> \infty exists and is, in fact, a Skyrme model; otherwise there is no continuum limit.Comment: Figures included (separate file). This ``replaced'' version corrects the discussion of backwards-in-time baryon

Floating Phase in 1D Transverse ANNNI Model

To study the ground state of ANNNI chain under transverse field as a function of frustration parameter $\kappa$ and field strength $\Gamma$, we present here two different perturbative analyses. In one, we consider the (known) ground state at $\kappa=0.5$ and $\Gamma=0$ as the unperturbed state and treat an increase of the field from 0 to $\Gamma$ coupled with an increase of $\kappa$ from 0.5 to $0.5+r\Gamma$ as perturbation. The first order perturbation correction to eigenvalue can be calculated exactly and we could conclude that there are only two phase transition lines emanating from the point $\kappa=0.5$, $\Gamma=0$. In the second perturbation scheme, we consider the number of domains of length 1 as the perturbation and obtain the zero-th order eigenfunction for the perturbed ground state. From the longitudinal spin-spin correlation, we conclude that floating phase exists for small values of transverse field over the entire region intermediate between the ferromagnetic phase and antiphase.Comment: 11 pages, 11 figure

Quantum Hall Ferrimagnetism in lateral quantum dot molecules

We demonstrate the existance of ferrimagnetic and ferromagnetic phases in a spin phase diagram of coupled lateral quantum dot molecules in the quantum Hall regime. The spin phase diagram is determined from Hartree-Fock Configuration Interaction method as a function of electron numbers N, magnetic field B, Zeeman energy, and tunneling barrier height. The quantum Hall ferrimagnetic phase corresponds to spatially imbalanced spin droplets resulting from strong inter-dot coupling of identical dots. The quantum Hall ferromagnetic phases correspond to ferromagnetic coupling of spin polarization at filling factors between $\nu=2$ and $\nu=1$.Comment: 4 pages, 4 figure

Exactly soluble model of interacting electrons

Journal ArticleWe diagonalize a many-fermion Hamiltonian consisting of terms quadratic as well as quartic in the field operators. A dual spectrum of eigenstates is an interesting result. We also derive a formula for obtaining the free energy at finite temperature