Threshold Singularities in the One Dimensional Hubbard Model

We consider excitations with the quantum numbers of a hole in the one dimensional Hubbard model below half-filling. We calculate the finite-size corrections to the energy. The results are then used to determine threshold singularities in the single-particle Green's function for commensurate fillings. We present the analogous results for the Yang-Gaudin model (electron gas with delta-function interactions).Comment: 26 pages, 12 figures version to appear in Phys Rev

Determinant formula for the six-vertex model with reflecting end

Using the Quantum Inverse Scattering Method for the XXZ model with open boundary conditions, we obtained the determinant formula for the six vertex model with reflecting end.Comment: 10 page

Relationship between single-particle excitation and spin excitation at the Mott Transition

An intuitive interpretation of the relationship between the dispersion relation of the single-particle excitation in a metal and that of the spin excitation in a Mott insulator is presented, based on the results for the one- and two-dimensional Hubbard models obtained by using the Bethe ansatz, dynamical density-matrix renormalization group method, and cluster perturbation theory. The dispersion relation of the spin excitation in the Mott insulator is naturally constructed from that of the single-particle excitation in the zero-doping limit in both one- and two-dimensional Hubbard models, which allows us to interpret the doping-induced states as the states that lose charge character toward the Mott transition. The characteristic feature of the Mott transition is contrasted with the feature of a Fermi liquid and that of the transition between a band insulator and a metal.Comment: 6 pages, 2 figures, to appear in JPS Conf. Pro

Dynamical Spin Response of Doped Two-Leg Hubbard-like Ladders

We study the dynamical spin response of doped two-leg Hubbard-like ladders in the framework of a low-energy effective field theory description given by the SO(6) Gross Neveu model. Using the integrability of the SO(6) Gross-Neveu model, we derive the low energy dynamical magnetic susceptibility. The susceptibility is characterized by an incommensurate coherent mode near $(\pi,\pi)$ and by broad two excitation scattering continua at other $k$-points. In our computation we are able to estimate the relative weights of these contributions. All calculations are performed using form-factor expansions which yield exact low energy results in the context of the SO(6) Gross-Neveu model. To employ this expansion, a number of hitherto undetermined form factors were computed. To do so, we developed a general approach for the computation of matrix elements of semi-local SO(6) Gross-Neveu operators. While our computation takes place in the context of SO(6) Gross-Neveu, we also consider the effects of perturbations away from an SO(6) symmetric model, showing that small perturbations at best quantitatively change the physics.Comment: 32 pages and 7 figure

Quantum phase transition in the one-dimensional extended Peierls-Hubbard model

We consider the one-dimensional extended Hubbard model in the presence of an explicit dimerization $\delta$. For a sufficiently strong nearest neighbour repulsion we establish the existence of a quantum phase transition between a mixed bond-order wave and charge-density wave phase from a pure bond-order wave phase. This phase transition is in the universality class of the two-dimensional Ising model.Comment: 6 pages, 3 figure

Thermodynamics of the one-dimensional half-filled Hubbard model in the spin-disordered regime

We analyze the Thermodynamic Bethe Ansatz equations of the one-dimensional half-filled Hubbard model in the "spin-disordered regime", which is characterized by the temperature being much larger than the magnetic energy scale but small compared to the Mott-Hubbard gap. In this regime the thermodynamics of the Hubbard model can be thought of in terms of gapped charged excitations with an effective dispersion and spin degrees of freedom that only contribute entropically. In particular, the internal energy and the effective dispersion become essentially independent of temperature. An interpretation of this regime in terms of a putative interacting-electron system at zero temperature leads to a metal-insulator transition at a finite interaction strength above which the gap opens linearly. We relate these observations to studies of the Mott-Hubbard transition in the limit of infinite dimensions.Comment: 15 pages, 3 figure

Dynamical response functions in the quantum Ising chain with a boundary

We determine dynamical response functions $<{\cal O}^\dagger(t,x_1){\cal O}(0,x_2)>$ in the scaling limit of the quantum Ising chain on the half line in the presence of a boundary magnetic field. Using a spectral representation in terms of infinite volume form factors and a boundary state, we derive an expansion for the correlator that is found to be rapidly convergent as long as |\frac{x_1+x_2}{\xi}|\agt 0.2 where $\xi$ is the correlation length. At sufficiently late times we observe oscillatory behaviour of the correlations arbitrarily far away from the boundary. We investigate the effects of the boundary bound state that is present for a range of boundary magnetic fields.Comment: 32 page

Effects of thermal phase fluctuations in a 2D superconductor: an exact result for the spectral function

We consider the single particle spectral function for a two-dimensional clean superconductor in a regime of strong critical thermal phase fluctuations. In the limit where the maximum of the superconducting gap is much smaller than the Fermi energy we obtain an exact expression for the spectral function integrated over the momentum component perpendicular to the Fermi surface.Comment: 4 pages, 3 figures. References added, figures improve

Optical conductivity of one-dimensional narrow-gap semiconductors

The optical conductivities of two one-dimensional narrow-gap semiconductors, anticrossing quantum Hall edge states and carbon nanotubes, are studied using bosonization method. A lowest order renormalization group analysis indicates that the bare band gap can be treated perturbatively at high frequency/temperature. At very low energy scale the optical conductivity is dominated by the excitonic contribution, while at temperature higher than a crossover temperature the excitonic features are eliminated by thermal fluctuations. In case of carbon nanotubes the crossover temperature scale is estimated to be 300 K.Comment: RevTeX4 file, 6 pages, no figur

Exactly Solvable Models of Strongly Correlated Electrons

This is a reprint volume devoted to exact solutions of models of strongly correlated electrons in one spatial dimension by means of the Bethe Ansatz.Comment: Editors 490 pages, World Scientific, 1994, ISBN 981-02-1534-