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 Magnetic Susceptibilities in Cu Benzoate

Recent experiments on the quasi 1-D antiferromagnet Cu Benzoate revealed a magentic field induced gap coexisting with (ferro)magnetic order. A theory explaining these findings has been proposed by Oshikawa and Affleck. In the present work we discuss consequences of this theory for inelastic neutron scattering experiments by calculating the dynamical magnetic susceptibilities close to the antiferromagnetic wave vector by the formfactor method.Comment: 6 pages of revtex, 9 figures, extended comparison with experimen

Applications of Massive Integrable Quantum Field Theories to Problems in Condensed Matter Physics

We review applications of the sine-Gordon model, the O(3) non-linear sigma model, the U(1) Thirring model, and the O(N) Gross--Neveu model to quasi one-dimensional quantum magnets, Mott insulators, and carbon nanotubes. We focus upon the determination of dynamical response functions for these problems. These quantities are computed by means of form factor expansions of quantum correlation functions in integrable quantum field theories. This approach is reviewed here in some detail.Comment: 150 pages, 35 figures, published in the I. Kogan Memorial Volume by World Scientifi

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

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

A Numerical Renormalization Group for Continuum One-Dimensional Systems

We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Kenneth Wilson's numerical renormalization group with Al. B. Zamolodchikov's truncated conformal spectrum approach. Key to the method is that such theories provide a set of completely understood eigenstates for which matrix elements can be exactly computed. In this procedure the RG flow of physical observables can be studied both numerically and analytically. To demonstrate the approach, we study the spectrum of a pair of coupled quantum Ising chains and correlation functions in a single quantum Ising chain in the presence of a magnetic field.Comment: 4 pages, 4 figure

"Light-cone" dynamics after quantum quenches in spin chains

Signal propagation in the non equilibirum evolution after quantum quenches has recently attracted much experimental and theoretical interest. A key question arising in this context is what principles, and which of the properties of the quench, determine the characteristic propagation velocity. Here we investigate such issues for a class of quench protocols in one of the central paradigms of interacting many-particle quantum systems, the spin-1/2 Heisenberg XXZ chain. We consider quenches from a variety of initial thermal density matrices to the same final Hamiltonian using matrix product state methods. The spreading velocities are observed to vary substantially with the initial density matrix. However, we achieve a striking data collapse when the spreading velocity is considered to be a function of the excess energy. Using the fact that the XXZ chain is integrable, we present an explanation of the observed velocities in terms of "excitations" in an appropriately defined generalized Gibbs ensemble.Comment: 4+pages, 5 figures, supplementary materia

Superconductivity generated by coupling to a Cooperon in a 2-dimensional array of 4-leg Hubbard ladders

Starting from an array of four-leg Hubbard ladders weakly doped away from half-filling and weakly coupled by inter-ladder tunneling, we derive an effective low energy model which contains a partially truncated Fermi surface and a well defined Cooperon excitation formed by a bound pair of holes. An attractive interaction in the Cooper channel is generated on the Fermi surface through virtual scattering into the Cooperon state. Although the model is derived in the weak coupling limit of a four-leg ladder array, an examination of exact results on finite clusters for the strong coupling t-J model suggests the essential features are also present for a strong coupling Hubbard model on a square lattice near half-filling.Comment: 20 pages, 4 figure

On the origin of the Fermi arc phenomena in the underdoped cuprates: signature of KT-type superconducting transition

We study the effect of thermal phase fluctuation on the electron spectral function $A(k,\omega)$ in a d-wave superconductor with Monte Carlo simulation. The phase degree of freedom is modeled by a XY-type model with build-in d-wave character. We find a ridge-like structure emerges abruptly on the underlying Fermi surface in $A(k,\omega=0)$ above the KT-transition temperature of the XY model. Such a ridge-like structure, which shares the same characters with the Fermi arc observed in the pseudogap phase of the underdoped cuprates, is found to be caused by the vortex-like phase fluctuation of the XY model.Comment: 5 page

Spectral Properties near the Mott Transition in the One-Dimensional Hubbard Model

Single-particle spectral properties near the Mott transition in the one-dimensional Hubbard model are investigated by using the dynamical density-matrix renormalization group method and the Bethe ansatz. The pseudogap, hole-pocket behavior, spectral-weight transfer, and upper Hubbard band are explained in terms of spinons, holons, antiholons, and doublons. The Mott transition is characterized by the emergence of a gapless mode whose dispersion relation extends up to the order of hopping t (spin exchange J) in the weak (strong) interaction regime caused by infinitesimal doping.Comment: 4 pages, 2 figure