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-

Threshold singularities in the dynamic response of gapless integrable models

We develop a method of an asymptotically exact treatment of threshold singularities in dynamic response functions of gapless integrable models. The method utilizes the integrability to recast the original problem in terms of the low-energy properties of a certain deformed Hamiltonian. The deformed Hamiltonian is local, hence it can be analysed using the conventional field theory methods. We apply the technique to spinless fermions on a lattice with nearest-neighbors repulsion, and evaluate the exponent characterizing the threshold singularity in the dynamic structure factor

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

Thermodynamics and excitations of the one-dimensional Hubbard model

We review fundamental issues arising in the exact solution of the one-dimensional Hubbard model. We perform a careful analysis of the Lieb-Wu equations, paying particular attention to so-called `string solutions'. Two kinds of string solutions occur: $\Lambda$ strings, related to spin degrees of freedom and $k-\Lambda$ strings, describing spinless bound states of electrons. Whereas $\Lambda$ strings were thoroughly studied in the literature, less is known about $k-\Lambda$ strings. We carry out a thorough analytical and numerical analysis of $k-\Lambda$ strings. We further review two different approaches to the thermodynamics of the Hubbard model, the Yang-Yang approach and the quantum transfer matrix approach, respectively. The Yang-Yang approach is based on strings, the quantum transfer matrix approach is not. We compare the results of both methods and show that they agree. Finally, we obtain the dispersion curves of all elementary excitations at zero magnetic field for the less than half-filled band by considering the zero temperature limit of the Yang-Yang approach.Comment: 72 pages, 11 figures, revte

Painlev\'e Transcendent Describes Quantum Correlation Function of the XXZ Antiferromagnet away from the free-fermion point

We consider quantum correlation functions of the antiferromagnetic spin-$\frac{1}{2}$ Heisenberg XXZ spin chain in a magnetic field. We show that for a magnetic field close to the critical field $h_c$ (for the critical magnetic field the ground state is ferromagnetic) certain correlation functions can be expressed in terms of the solution of the Painlev\'e V transcendent. This establishes a relation between solutions of Painlev\'e differential equations and quantum correlation functions in models of {\sl interacting} fermions. Painlev\'e transcendents were known to describe correlation functions in models with free fermionic spectra.Comment: 10 pages, LaTeX2

Correlation functions of the one-dimensional attractive Bose gas

The zero-temperature correlation functions of the one-dimensional attractive Bose gas with delta-function interaction are calculated analytically for any value of the interaction parameter and number of particles, directly from the integrability of the model. We point out a number of interesting features, including zero recoil energy for large number of particles, analogous to a M\"ossbauer effect.Comment: 4 pages, 2 figure

Maxwell-Bloch equation and Correlation function for penetrable Bose gas

We consider the quantum nonlinear Schr\"odinger equation in one space and one time dimension. We are interested in the non-free-fermionic case. We consider static temperature-dependent correlation functions. The determinant representation for correlation functions simplifies in the small mass limit of the Bose particle. In this limit we describe the correlation functions by the vacuum expectation value of a boson-valued solution for Maxwell-Bloch differential equation. We evaluate long-distance asymptotics of correlation functions in the small mass limit.Comment: LaTEX file, 20 pages, to appear J. Phys. A (1997

Dynamical density correlation function of 1D Mott insulators in a magnetic field

We consider the one dimensional (1D) extended Hubbard model at half filling in the presence of a magnetic field. Using field theory techniques we calculate the dynamical density-density correlation function $\chi_{nn}(\omega,q)$ in the low-energy limit. When excitons are formed, a singularity appears in $\chi_{nn}(\omega,q)$ at a particular energy and momentum transfer.Comment: 7 pages, 4 figure