J. M. P. Carmelo

One-electron singular branch lines of the Hubbard chain

The momentum and energy dependence of the weight distribution in the vicinity of the one-electron spectral-function singular branch lines of the 1D Hubbard model is studied for all values of the electronic density and on-site repulsion U. To achieve this goal, we use the recently introduced pseudofermion dynamical theory. Our predictions agree quantitatively for the whole momentum and energy bandwidth with the peak dispersions observed by angle-resolved photoelectron spectroscopy in the quasi-1D organic conductor TTF-TCNQ.

Spinon and η-spinon correlation functions of the Hubbard chain

We calculate real-space static correlation functions related to basic entities of the one-dimensional Hubbard model, which emerge from the exact Betheansatz solution. These entities involve complex rearrangements of the original electrons. Basic ingredients are operators related to unoccupied, singly occupied with spin up or spin down and doubly occupied sites. The spatial decay of their correlation functions is determined using an approximate mean-field-like approach based on the Zou-Anderson transformation and DMRG results for the half-filled case. The nature and spatial extent of the correlations between two sites on the Hubbard chain is studied using the eigenstates and eigenvalues of the two-site reduced density matrix. PACS numbers: 71.10.Fd, 71.10.Pm, 73.90.+f

Charge and spin quantum fluids generated by many-electron interactions

Abstract In this paper we describe the electrons of the non-perturbative one-dimensional (1D) Hubbard model by a fluid of unpaired rotated electrons and a fluid of zero-spin rotated-electron pairs. The rotated electrons are related to the original electrons by a mere unitary transformation. For all finite values of energy and for the whole parameter space of the model this two-fluid picture leads to a description of the energy eigenstates in terms of occupancy configurations of η-spin 1/2 holons, spin 1/2 spinons, and c pseudoparticles only. The electronic degrees of freedom couple to external charge (and spin) probes through the holons and c pseudoparticles (and spinons). Our results refer to very large values of the number of lattice sites Na. The holon (and spinon) charge (and spin) transport is made by 2ν-holon (and 2ν-spinon) composite pseudoparticles such that ν=1,2,… . For electronic numbers obeying the inequalities N⩽Na and N↓⩽N↑ there are no zero-spin rotated-electron pairs in the ground state and the unpaired-rotated-electron fluid is described by a charge c pseudoparticle fluid and a spin ν=1 two-spinon pseudoparticle fluid. The spin two-spinon pseudoparticle fluid is the 1D realization of the two-dimensional resonating valence bond spin fluid.

Finite-energy Landau liquid theory for the one-dimensional Hubbard model: Pseudoparticle energy bands and degree of localization/delocalization

In this paper we consider the one-dimensional Hubbard model and study the deviations from the ground-state values of double occupation which result from creation or annihilation of holons, spinons, and pseudoparticles. These quantum objects are such that all energy eigenstates are described by their occupancy configurations. The band-momentum dependence of the obtained double-occupation spectra provides important information on the degree of localization/delocalization of the real-space lattice electron site distribution configurations associated with the pseudoparticles. We also study the band momentum, on-site electronic repulsion, and electronic density dependence of the pseudoparticle energy bands. The shape of these bands plays an important role in the finite-energy spectral properties of the model. Such a shape defines the form of the lines in the momentum-energy/frequency plane where the peaks and edges of the one-electron and two-electron spectral weight of physical operators are located. Our findings are useful for the study of the one-electron and two-electron spectral-weight distribution of physical operators.

Dynamical functions of a 1D correlated quantum liquid

The dynamical correlation functions in one-dimensional electronic systems show power-law behaviour at low energies and momenta close to integer multiples of the charge and spin Fermi momenta. These systems are usually referred to as Tomonaga?Luttinger liquids. However, near well defined lines of the (k,?) plane the power-law behaviour extends beyond the low-energy cases mentioned above, and also appears at higher energies, leading to singular features in the photoemission spectra and other dynamical correlation functions. The general spectral-function expressions derived in this paper were used in recent theoretical studies of the finite-energy singular features in photoemission of the organic compound tetrathiafulvalene?tetracyanoquinodimethane (TTF-TCNQ) metallic phase. They are based on a so-called pseudofermion dynamical theory (PDT), which allows us to systematically enumerate and describe the excitations in the Hubbard model starting from the Bethe ansatz, as well as to calculate the charge and spin object phase shifts appearing as exponents of the power laws. In particular, we concentrate on the spin-density limit and on effects in the vicinity of the singular border lines, as well as close to half filling. Our studies take into account spectral contributions from types of microscopic processes that do not occur for finite values of the spin density. In addition, the specific processes involved in the spectral features of TTF-TCNQ are studied. Our results are useful for the further understanding of the unusual spectral properties observed in low-dimensional organic metals and also provide expressions for the one-?and two-atom spectral functions of a correlated quantum system of ultracold fermionic atoms in a 1D optical lattice with on-site two-atom repulsion.

Electronic structure of the quasi-one-dimensional organic conductor TTF-TCNQ

Abstract We present an investigation of the electronic structure of a prototypical quasi-one-dimensional conductor, the organic compound TTF-TCNQ, by means of angle-resolved photoemission spectroscopy. By comparison with LDA-band structure calculations we identify significant deviations between experiment and theory. We discuss possible origins for these deviations in terms of electronic correlations and surface effects in this material.

Finite-temperature transport in finite-size Hubbard rings in the strong-coupling limit

We study the current, the curvature of levels, and the finite temperature charge stiffness, D(T,L), in the strongly correlated limit, U>>t, for Hubbard rings of L sites, with U the on-site Coulomb repulsion and t the hopping integral. Our study is done for finite-size systems and any band filling. Up to order t we derive our results following two independent approaches, namely, using the solution provided by the Bethe ansatz and the solution provided by an algebraic method, where the electronic operators are represented in a slave-fermion picture. We find that, in the U=\infty case, the finite-temperature charge stiffness is finite for electronic densities, n, smaller than one. These results are essencially those of spinless fermions in a lattice of size L, apart from small corrections coming from a statistical flux, due to the spin degrees of freedom. Up to order t, the Mott-Hubbard gap is \Delta_{MH}=U-4t, and we find that D(T) is finite for n<1, but is zero at half-filling. This result comes from the effective flux felt by the holon excitations, which, due to the presence of doubly occupied sites, is renormalized to \Phi^{eff}=\phi(N_h-N_d)/(N_d+N_h), and which is zero at half-filling, with N_d and N_h being the number of doubly occupied and empty lattice sites, respectively. Further, for half-filling, the current transported by any eigenstate of the system is zero and, therefore, D(T) is also zero.

Strongly correlated systems, coherence and entanglement

Strongly Correlated Systems: Spin Glasses (I R Pimentel) Double Exchange Models with Disorder (V Pereira et al.) Anomalous Hall Effect in Magnetic Nanostructures (V K Dugaev et al.) Introduction to the Physics of Graphene (E Vieira de Castro et al.) Dynamics and Domain Growth in Quantum Spin Systems (V Turkowski & V Rocha Vieira) Coherence in Macroscopic Systems: Atomic Bose-Einstein Condensates: Beyond Mean Field Theory (G Nunes) Critical Fields in Superconductors with Singular Density of States (R G Dias) Chiral Symmetry and BCS (J E Ribeiro) Quantum Entanglement: Entanglement in Quantum Phase Transitions (Y Omar et al.) Macroscopic Entanglement at Finite Temperature (Y Omar et al.) and other papers.

The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

Abstract The momentum bands, energy dispersions, and velocities of the charge c fermions and spin-neutral two-spinon s1 fermions of a square-lattice quantum liquid referring to the Hubbard model on such a lattice of edge length L in the one- and two-electron subspace are studied. The model involves the effective nearest-neighbor integral t and on-site repulsion U and can be experimentally realized in systems of correlated ultra-cold fermionic atoms on an optical lattice and thus our results are of interest for such systems. Our investigations profit from a general rotated-electron description, which is consistent with the model global SO ( 3 ) × SO ( 3 ) × U ( 1 ) symmetry. For the model in the one- and two-electron subspace the discrete momentum values of the c and s1 fermions are good quantum numbers so that in contrast to the original strongly-correlated electronic problem their interactions are residual. The use of our description renders an involved many-electron problem into a quantum liquid with some similarities with a Fermi liquid. For the Hubbard model on a square lattice in the one- and two-electron subspace a composite s1 fermion consists of a spin-singlet spinon pair plus an infinitely thin flux tube attached to it. In the U / 4 t → ∞ limit of infinite on-site interaction the c fermions become non-interacting spinless fermions and the s1 fermion occupancy configurations that generate the spin degrees of freedom of spin-density m = 0 ground states become within a suitable mean-field approximation for the fictitious magnetic field B s 1 e → x 3 brought about by the correlations of the original N electron problem those of a full lowest Landau level with N / 2 degenerate one-s1 fermion states of the two-dimensional quantum Hall effect. In turn, for U / 4 t finite the degeneracy of the N / 2 one-s1-fermion states is removed by the emergence of a finite-energy-bandwidth s1 fermion dispersion yet the number of s1 band discrete momentum values remains being given by B s 1 L 2 / Φ 0 and the s1 effective lattice spacing by a s 1 = l s 1 / 2 π where l s 1 is the fictitious-magnetic-field length and in our units the fictitious-magnetic-field flux quantum reads Φ 0 = 1 . Elsewhere it is found that the use of the square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions investigated here contributes to the further understanding of the role of electronic correlations in the unusual properties of the hole-doped cuprate superconductors. This indicates that quantum-Hall-type behavior with or without magnetic field may be ubiquitous in nature.

Charge dynamics in half-filled Hubbard chains with finite on-site interaction

We study the charge dynamic structure factor of the one-dimensional Hubbard model with finite on-site repulsion U at half filling. Numerical results from the time-dependent density matrix renormalization group are analyzed by comparison with the exact spectrum of the model. The evolution of the line shape as a function of U is explained in terms of a relative transfer of spectral weight between the two-holon continuum that dominates in the limit U\to \infty and a subset of the two-holon-two-spinon continuum that reconstructs the electron-hole continuum in the limit U\to 0. Power-law singularities along boundary lines of the spectrum are described by effective impurity models that are explicitly invariant under spin and \eta-spin SU(2) rotations. The Mott-Hubbard metal-insulator transition is reflected in a discontinuous change of the exponents of edge singularities at U=0. The sharp feature observed in the spectrum for momenta near the zone boundary is attributed to a Van Hove singularity that persists as a consequence of integrability.