13,301 research outputs found
Thermodynamic Bethe Ansatz for N = 1 Supersymmetric Theories
We study a series of supersymmetric integrable particle theories in
dimensions. These theories are represented as integrable perturbations
of specific superconformal field theories. Starting from the
conjectured -matrices for these theories, we develop the Thermodynamic Bethe
Ansatz (TBA), where we use that the 2-particle -matrices satisfy a free
fermion condition. Our analysis proves a conjecture by E.~Melzer, who proposed
that these supersymmetric TBA systems are ``folded'' versions of
supersymmetric TBA systems that were first studied by P.~Fendley and
K.~Intriligator.Comment: 24 pages, Revte
Edge states in graphene quantum dots: Fractional quantum Hall effect analogies and differences at zero magnetic field
We investigate the way that the degenerate manifold of midgap edge states in
quasicircular graphene quantum dots with zig-zag boundaries supports, under
free-magnetic-field conditions, strongly correlated many-body behavior
analogous to the fractional quantum Hall effect (FQHE), familiar from the case
of semiconductor heterostructures in high magnetic fields. Systematic
exact-diagonalization (EXD) numerical studies are presented for the first time
for 5 <= N <= 8 fully spin-polarized electrons and for total angular momenta in
the range of N(N-1)/2 <= L <= 150. We present a derivation of a
rotating-electron-molecule (REM) type wave function based on the methodology
introduced earlier [C. Yannouleas and U. Landman, Phys. Rev. B 66, 115315
(2002)] in the context of the FQHE in two-dimensional semiconductor quantum
dots. The EXD wave functions are compared with FQHE trial functions of the
Laughlin and the derived REM types. It is found that a variational extension of
the REM offers a better description for all fractional fillings compared with
that of the Laughlin functions (including total energies and overlaps), a fact
that reflects the strong azimuthal localization of the edge electrons. In
contrast with the multiring arrangements of electrons in circular semiconductor
quantum dots, the graphene REMs exhibit in all instances a single (0,N)
polygonal-ring molecular (crystalline) structure, with all the electrons
localized on the edge. Disruptions in the zig-zag boundary condition along the
circular edge act effectively as impurities that pin the electron molecule,
yielding single-particle densities with broken rotational symmetry that portray
directly the azimuthal localization of the edge electrons.Comment: Revtex. 14 pages with 13 figures and 2 tables. Physical Review B, in
press. For related papers, see http://www.prism.gatech.edu/~ph274cy
Low energy excitations of double quantum dots in the lowest Landau level regime
We study the spectrum and magnetic properties of double quantum dots in the
lowest Landau level for different values of the hopping and Zeeman parameters
by means of exact diagonalization techniques in systems of N=6 and N=7
electrons and filling factor close to 2. We compare our results with those
obtained in double quantum layers and single quantum dots. The Kohn theorem is
also discussed.Comment: 23 pages, 4 figures, 1 table; references added; journal versio
Quantum dots in high magnetic fields: Rotating-Wigner-molecule versus composite-fermion approach
Exact diagonalization results are reported for the lowest rotational band of
N=6 electrons in strong magnetic fields in the range of high angular momenta 70
<= L <= 140 (covering the corresponding range of fractional filling factors 1/5
>= nu >= 1/9). A detailed comparison of energetic, spectral, and transport
properties (specifically, magic angular momenta, radial electron densities,
occupation number distributions, overlaps and total energies, and exponents of
current-voltage power law) shows that the recently discovered
rotating-electron-molecule wave functions [Phys. Rev. B 66, 115315 (2002)]
provide a superior description compared to the
composite-fermion/Jastrow-Laughlin ones.Comment: Extensive clarifications were added (see new footnotes) regarding the
difference between the rotating Wigner molecule and the bulk Wigner crystal;
also regarding the influence of an external confining potential. 12 pages.
Revtex4 with 6 EPS figures and 5 tables . For related papers, see
http://www.prism.gatech.edu/~ph274c
Geometrical Lattice models for N=2 supersymmetric theories in two dimensions
We introduce in this paper two dimensional lattice models whose continuum
limit belongs to the series. The first kind of model is integrable and
obtained through a geometrical reformulation, generalizing results known in the
case, of the vertex models (based on the quantum algebra
and representation of spin ). We demonstrate in particular
that at the point, the free energy of the vertex model can
be obtained exactly by counting arguments, without any Bethe ansatz
computation, and we exhibit lattice operators that reproduce the chiral ring.
The second class of models is more adequately described in the language of
twisted supersymmetry, and consists of an infinite series of
multicritical polymer points, which should lead to experimental realizations.
It turns out that the exponents for these multicritical
polymer points coincide with old phenomenological formulas due to the chemist
Flory. We therefore confirm that these formulas are {\bf exact} in two
dimensions, and suggest that their unexpected validity is due to non
renormalization theorems for the underlying theories. We also discuss the
status of the much discussed theta point for polymers in the light of
renormalization group flows.Comment: 23 pages (without figures
Electrons in a Strong Magnetic Field on a Disk
The problem of interacting electrons moving under the influence of a strong
magnetic field in two dimensions on a finite disk is reconsidered. First, the
results of exact diagonalizations for up to electrons for Coulomb as well
as for a short--range interaction are used in the search for a peculiar ground
state corresponding to filling factor . Not for the Coulomb, but only for
the short--range interaction, can the --state be safely identified amongst
the spectra of various filling factors close to . Second, the propositions
of the concept of quasiparticles, as used in the hierarchical theory, are
examined in view of the exact results for the disk geometry. Whereas the theory
for the quasiholes is in complete accordance with the spectra, for the
quasielectrons, finite size corrections make an analysis difficult. For the
quasielectron energy, an extrapolation to is given and
compared with the corresponding extrapolations of three different proposals for
trial wave functions. While the limiting value for the best trial wave function
is very close to the limit of the exact results, the behavior of the finite
size corrections of the exact energies and of the trial wave functions,
respectively, is qualitatively rather different.Comment: 24 pages, 6 figures available upon request from W. Apel, LaTe
Theoretical study of the thermal behavior of free and alumina-supported Fe-C nanoparticles
The thermal behavior of free and alumina-supported iron-carbon nanoparticles
is investigated via molecular dynamics simulations, in which the effect of the
substrate is treated with a simple Morse potential fitted to ab initio data. We
observe that the presence of the substrate raises the melting temperature of
medium and large nanoparticles ( = 0-0.16, = 80-1000, non-
magic numbers) by 40-60 K; it also plays an important role in defining the
ground state of smaller Fe nanoparticles ( = 50-80). The main focus of our
study is the investigation of Fe-C phase diagrams as a function of the
nanoparticle size. We find that as the cluster size decreases in the
1.1-1.6-nm-diameter range the eutectic point shifts significantly not only
toward lower temperatures, as expected from the Gibbs-Thomson law, but also
toward lower concentrations of C. The strong dependence of the maximum C
solubility on the Fe-C cluster size may have important implications for the
catalytic growth of carbon nanotubes by chemical vapor deposition.Comment: 13 pages, 11 figures, higher quality figures can be seen in article 9
at http://alpha.mems.duke.edu/wahyu
Complete Bethe Ansatz solution of the open spin-s XXZ chain with general integrable boundary terms
We consider the open spin-s XXZ quantum spin chain with N sites and general
integrable boundary terms for generic values of the bulk anisotropy parameter,
and for values of the boundary parameters which satisfy a certain constraint.
We derive two sets of Bethe Ansatz equations, and find numerical evidence that
together they give the complete set of eigenvalues of the transfer
matrix. For the case s=1, we explicitly determine the Hamiltonian, and find an
expression for its eigenvalues in terms of Bethe roots.Comment: 23 pages -- Latex2e; misprints in appendix correcte
Persistent peri-Heptacene: Synthesis and In Situ Characterization
n-peri-Acenes (n-PAs) have gained interest as model systems of zigzag-edged graphene nanoribbons for potential applications in nanoelectronics and spintronics. However, the synthesis of n-PAs larger than peri-tetracene remains challenging because of their intrinsic open-shell character and high reactivity. Presented here is the synthesis of a hitherto unknown n-PA, that is, peri-heptacene (7-PA), in which the reactive zigzag edges are kinetically protected with eight 4-tBu-C6H4 groups. The formation of 7-PA is validated by high-resolution mass spectrometry and in situ FT-Raman spectroscopy. 7-PA displays a narrow optical energy gap of 1.01 eV and exhibits persistent stability (t1/2≈25 min) under inert conditions. Moreover, electron-spin resonance measurements and theoretical studies reveal that 7-PA exhibits an open-shell feature and a significant tetraradical character. This strategy could be considered a modular approach for the construction of next-generation (3 N+1)-PAs (where N≥3). © 2021 The Authors. Angewandte Chemie International Edition published by Wiley-VCH Gmb
The massless supersymmetric ladder with L rungs
We show that in the massless N=1 supersymmetric Wess-Zumino theory it is
possible to devise a computational strategy by which the x-space calculation of
the ladder 4-point correlators can be carried out without introducing any
regularization. As an application we derive a representation valid at all loop
orders in terms of conformal invariant integrals. We obtain an explicit
expression of the 3-loop ladder diagram for collinear external points.Comment: LaTeX, 17 pages, 8 figure
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