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 ``$c$'' and ``$s$'' separation. Here $c$ and $s$ 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 $c$ and $s$ elementary excitations are associated with the $c$ and $s$ 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 $c$ and $s$ 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 $\uparrow$ and $\downarrow$ quasiparticles recombine the pseudoparticle colors $c$ and $s$ (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 1$<$D$<$3. However, whether the electron -- quasiparticle overlap can vanish in D$>$1 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 $U$, 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 $n1$), 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 $\eta$-spin-zero $2\nu$-holon composite objects, spin-zero $2\nu$-spinon composite objects, and charged $\eta$-spin-less and spin-less objects, rather than by the scattering of independent $\eta$-spin 1/2 holons and spin 1/2 spinons. Here $\nu =1,2,...$. The corresponding $S$ 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 $U$ 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]

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 Tecnología DIP2003-0666-02-