870 research outputs found
Magnetic-field and chemical-potential effects on the low-energy separation
We show that in the presence of a magnetic field the usual low-energy
separation of the Hubbard chain is replaced by a ``'' and ``''
separation. Here and refer to small-momentum and low-energy independent
excitation modes which couple both to charge and spin. Importantly, we find the
exact generators of these excitations both in the electronic and pseudoparticle
basis. In the limit of zero magnetic field these generators become the usual
charge and spin fluctuation operators. The and elementary excitations
are associated with the and pseudoparticles, respectively. We also
study the separate pseudoparticle left and right conservation laws. In the
presence of the magnetic field the small-momentum and low-energy excitations
can be bosonized. However, the suitable bosonization corresponds to the and
pseudoparticle modes and not to the usual charge and spin fluctuations. We
evaluate exactly the commutator between the electronic-density operators. Its
spin-dependent factor is in general non diagonal and depends on the
interaction. The associate bosonic commutation relations characterize the
present unconventional low-energy separation.Comment: 29 pages, latex, submitted to Phys. Rev.
Electrons, pseudoparticles, and quasiparticles in the one-dimensional many-electron problem
We generalize the concept of quasiparticle for one-dimensional (1D)
interacting electronic systems. The and
quasiparticles recombine the pseudoparticle colors and (charge and spin
at zero magnetic field) and are constituted by one many-pseudoparticle {\it
topological momenton} and one or two pseudoparticles. These excitations cannot
be separated. We consider the case of the Hubbard chain. We show that the
low-energy electron -- quasiparticle transformation has a singular charater
which justifies the perturbative and non-perturbative nature of the quantum
problem in the pseudoparticle and electronic basis, respectively. This follows
from the absence of zero-energy electron -- quasiparticle overlap in 1D. The
existence of Fermi-surface quasiparticles both in 1D and three dimensional (3D)
many-electron systems suggests there existence in quantum liquids in dimensions
1D3. However, whether the electron -- quasiparticle overlap can vanish in
D1 or whether it becomes finite as soon as we leave 1D remains an unsolved
question.Comment: 43 pages, latex, no figures, submitted to Physical Review
Conservation laws and bosonization in integrable Luttinger liquids
We examine and explain the Luttinger-liquid character of models solvable by
the Bethe ansatz by introducing a suitable bosonic operator algebra. In the
case of the Hubbard chain, this involves two bosonic algebras which apply to
{\it all} values of , electronic density, and magnetization. Only at zero
magnetization does this lead to the usual charge - spin separation. We show
that our ``pseudoparticle'' operator approach clarifies, unifies, and extends
several recent results, including the existence of independent right and left
equations of motion and the concept of ``pseudoparticle'' (also known as
``Bethe quasiparticle'').Comment: 12 pages, RevTeX, preprint CSI
Ground states of integrable quantum liquids
Based on a recently introduced operator algebra for the description of a
class of integrable quantum liquids we define the ground states for all
canonical ensembles of these systems. We consider the particular case of the
Hubbard chain in a magnetic field and chemical potential. The ground states of
all canonical ensembles of the model can be generated by acting onto the
electron vacuum (densities ), suitable
pseudoparticle creation operators. We also evaluate the energy gaps of the
non-lowest-weight states (non - LWS's) and non-highest-weight states (non -
HWS's) of the eta-spin and spin algebras relative to the corresponding ground
states. For all sectors of parameter space and symmetries the {\it exact ground
state} of the many-electron problem is in the pseudoparticle basis the
non-interacting pseudoparticle ground state. This plays a central role in the
pseudoparticle perturbation theory.Comment: RevteX 3.0, 43 pages, preprint Univ.Evora, Portuga
Scattering mechanisms and spectral properties of the one-dimensional Hubbard model
It is found that the finite-energy spectral properties of the one-dimensional
Hubbard model are controlled by the scattering of charged -spin-zero
-holon composite objects, spin-zero -spinon composite objects, and
charged -spin-less and spin-less objects, rather than by the scattering
of independent -spin 1/2 holons and spin 1/2 spinons. Here . The corresponding matrix is calculated and its relation to the
spectral properties is clarified.Comment: 8 pages, no figure
Instabilities of the Hubbard chain in a magnetic field
We find and characterize the instabilities of the repulsive Hubbard chain in
a magnetic field by studing all response functions at low frequency \omega and
arbitrary momentum. The instabilities occur at momenta which are simple
combinations of the (U=0) \sigma =\uparrow ,\downarrow Fermi points, \pm
k_{F\sigma}. For finite values of the on-site repulsion U the instabilities
occur for single \sigma electron adding or removing at momenta \pm k_{F\sigma},
for transverse spin-density wave (SDW) at momenta \pm 2k_F (where
2k_F=k_{F\uparrow}+k_{F\downarrow}), and for charge-density wave (CDW) and SDW
at momenta \pm 2k_{F\uparrow} and \pm 2k_{F\downarrow}. While at zero magnetic
field removing or adding single electrons is dominant, the presence of that
field brings about a dominance for the transverse \pm 2k_F SDW over all the
remaining instabilities for a large domain of and density n values. We go
beyond conformal-field theory and study divergences which occur at finite
frequency in the one-electron Green function at half filling and in the
transverse-spin response function in the fully-polarized ferromagnetic phase.Comment: LaTeX file, 15 pages plus 9 figures. Accepted for publication in
Phys. Rev. B. The figures can be obtained upon request from Pedro Sacramento
at [email protected]
Chapter Two Democratization of the Legislative Executive, and Judicial Departments of Government
New perturbation theory of low-dimensional quantum liquids II: operator description of Virasoro algebras in integrable systems
We show that the recently developed {\it pseudoparticle operator algebra}
which generates the low-energy Hamiltonian eigenstates of multicomponent
integrable systems also provides a natural operator representation for the the
Virasoro algebras associated with the conformal-invariant character of the
low-energy spectrum of the these models. Studying explicitly the Hubbard chain
in a non-zero chemical potential and external magnetic field, we establish that
the pseudoparticle perturbation theory provides a correct starting point for
the construction of a suitable critical-point Hamiltonian. We derive explicit
expressions in terms of pseudoparticle operators for the generators of the
Virasoro algebras and the energy-momentum tensor, describe the
conformal-invariant character of the critical point from the point of view of
the response to curvature of the two-dimensional space-time, and discuss the
relation to Kac-Moody algebras and dynamical separation.Comment: 35 pages, RevteX, preprint UA
Improving the Computational Efficiency in Symmetrical Numeric Constraint Satisfaction Problems
Models are used in science and engineering for experimentation,
analysis, diagnosis or design. In some cases, they can be considered
as numeric constraint satisfaction problems (NCSP). Many models
are symmetrical NCSP. The consideration of symmetries ensures that
NCSP-solver will find solutions if they exist on a smaller search space.
Our work proposes a strategy to perform it. We transform the symmetrical
NCSP into a newNCSP by means of addition of symmetry-breaking
constraints before the search begins. The specification of a library of possible
symmetries for numeric constraints allows an easy choice of these
new constraints. The summarized results of the studied cases show the
suitability of the symmetry-breaking constraints to improve the solving
process of certain types of symmetrical NCSP. Their possible speedup
facilitates the application of modelling and solving larger and more
realistic problems.Ministerio de Ciencia y TecnologĂa DIP2003-0666-02-
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