3,803 research outputs found
Interacting Electrons on a Square Fermi Surface
Electronic states near a square Fermi surface are mapped onto quantum chains.
Using boson-fermion duality on the chains, the bosonic part of the interaction
is isolated and diagonalized. These interactions destroy Fermi liquid behavior.
Non-boson interactions are also generated by this mapping, and give rise to a
new perturbation theory about the boson problem. A case with strong repulsions
between parallel faces is studied and solved. There is spin-charge separation
and the square Fermi surface remains square under doping. At half-filling,
there is a charge gap and insulating behavior together with gapless spin
excitations. This mapping appears to be a general tool for understanding the
properties of interacting electrons on a square Fermi surface.Comment: 25 pages, Nordita preprint 94/22
Matrix methods for calculating zeros, coefficients, Christoffel numbers, and derivatives of some orthogonal polynomials
Jacobi matrix method for calculating zeros, coefficients, Christoffel numbers, and derivatives of orthogonal polynomial
A scale-model room as a practical teaching experiment
A practical experiment is described which was used to help university students increase their understanding of the effect of construction methods and window design on passive solar heating and electrical heating. A number of one tenth scale model rooms were constructed by students and sited out-of-doors in the late autumn. The models were fabricated to mimic available commercial construction techniques with careful consideration being given to window size and placement for solar access. Each model had a thermostatically controlled electric heating element. The temperatures and electricity use of the models were recorded using data-loggers over a two week period. The performances of the models based on energy consumption and internal temperature were compared with each other and with predictions based upon thermal mass and R-values. Examples of questions used by students to facilitate this process are included. The effect of scaling on thermal properties was analysed using Buckingham’s p-theorem.<br /
Adjacent face scattering of electrons on a square Fermi surface
Interacting electrons with a square Fermi surface is investigated from a
bosonic point of view taking into account electron scattering between all faces
of the square. Fermion operators are classified according to their dimensions
and the stability of the boson fixed-point is investigated. In particular we
find, in contrast to previous studies, that the square Fermi surface is
unstable to doping in the case of no spin gap and microscopic Hubbard
interactions.Comment: Revtex 6 pages, 1 Figur
Field-theoretical renormalization group for a flat two-dimensional Fermi surface
We implement an explicit two-loop calculation of the coupling functions and
the self-energy of interacting fermions with a two-dimensional flat Fermi
surface in the framework of the field theoretical renormalization group (RG)
approach. Throughout the calculation both the Fermi surface and the Fermi
velocity are assumed to be fixed and unaffected by interactions. We show that
in two dimensions, in a weak coupling regime, there is no significant change in
the RG flow compared to the well-known one-loop results available in the
literature. However, if we extrapolate the flow to a moderate coupling regime
there are interesting new features associated with an anisotropic suppression
of the quasiparticle weight Z along the Fermi surface, and the vanishing of the
renormalized coupling functions for several choices of the external momenta.Comment: 16 pages and 22 figure
Equations for Runge-kutta Formulas Through the Eighth Order
Tables for elementary weights of Runge-Kutta formulas of first eight orders and for relations of explicit formulas through order seve
Nonuniversal spectral properties of the Luttinger model
The one electron spectral functions for the Luttinger model are discussed for
large but finite systems. The methods presented allow a simple interpretation
of the results. For finite range interactions interesting nonunivesal spectral
features emerge for momenta which differ from the Fermi points by the order of
the inverse interaction range or more. For a simplified model with interactions
only within the branches of right and left moving electrons analytical
expressions for the spectral function are presented which allows to perform the
thermodynamic limit. As in the general spinless model and the model including
spin for which we present mainly numerical results the spectral functions do
not approach the noninteracting limit for large momenta. The implication of our
results for recent high resolution photoemission measurements on quasi
one-dimensional conductors are discussed.Comment: 19 pages, Revtex 2.0, 5 ps-figures, to be mailed on reques
Excitations in one-dimensional S=1/2 quantum antiferromagnets
The transition from dimerized to uniform phases is studied in terms of
spectral weights for spin chains using continuous unitary transformations
(CUTs). The spectral weights in the S=1 channel are computed perturbatively
around the limit of strong dimerization. We find that the spectral weight is
concentrated mainly in the subspaces with a small number of elementary triplets
(triplons), even for vanishing dimerization. So, besides spinons, triplons may
be used as elementary excitations in spin chains. We conclude that there is no
necessity to use fractional excitations in low-dimensional, undoped or doped
quantum antiferromagnets.Comment: 4 pages, 1 figure include
Spin-density wave versus superconducting fluctuations for quasi-one-dimensional electrons in two chains of Tomonaga-Luttinger liquids
We study possible states at low temperatures by applying the
renormalization-group method to two chains of Tomonaga-Luttinger liquids with
both repulsive intrachain interactions and interchain hopping. As the energy
decreases below the hopping energy, three distinct regions I, III, and II
appear successively depending on properties of fluctuations. The crossover from
the spin-density wave (SDW) state to superconducting (SC) state takes place in
region III where there are the excitation gaps of transverse charge and spin
fluctuations. The competition between SDW and SC states in region III is
crucial to understanding the phase diagram in the quasi-one-dimensional organic
conductors.Comment: 11 pages, Revtex format, 1 figure, to be published in Phys. Rev.
Correlation functions for a two-dimensional electron system with bosonic interactions and a square Fermi surface
We calculate zero-temperature correlation functions for a model of 2D
interacting electrons with short-range interactions and a square Fermi surface.
The model was arrived at by mapping electronic states near a square Fermi
surface with Hubbard-like interactions onto one-dimensional quantum chains,
retaining terms which can be written in terms of bosonic density operators.
Interactions between orthogonal chains, corresponding to orthogonal faces of
the square Fermi surface, are neglected. The correlation functions become sums
of Luttinger-type correlation functions due to the bosonic model. However, the
correlation function exponents differ in form from those of the Luttinger
model. As a consequence, the simple scaling relations found to exist between
the Luttinger model exponents, do not carry over to the leading exponents of
our model. We find that for repulsive effective interactions, charge-density
wave/spin-density wave instabilities are dominant. We do not consider d-wave
instabilities here.Comment: 12 pages, no figures; to be published in Physical Review
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