Hydrodynamic Formulation of the Hubbard Model

Recently Tsai et.al. (cond-mat/0406174) have used the renormalization group approach to study strong coupling superconductors without assuming a broken symmetry phase. We use the hydrodynamic formulation to study the same problem with the same intention. We recast the electron-phonon + electron-electron problem in the hydrodynamic language and compute the one-particle electron Green function at finite temperature. From this we extract the dynamical density of states at fi...

This work deals with the one-dimensional Hubbard model. It has seven chapters: 1. Introduction; 2. The Hubbard Model; 3. Algebraic Representation for the Hilbert Space of the 1D Hubbard Model; 4. Pseudoparticle Perturbation Theory; 5. Excitations and Finite-Size Effects; 6. Zero-Temperature Transport; 7. Conclusions.

We have studied nonequilibrium dynamics of the one-dimensional Hubbard model using the generalized hydrodynamic theory. We mainly investigated the spatio-temporal profile of charge density, energy density and their currents using the partitioning protocol; the initial state consists of two semi-infinite different thermal equilibrium states joined at the origin. In this protocol, there appears around the origin a transient region where currents flow. We examined how density an...

We use tools from integrability and generalized hydrodynamics to study finite-temperature dynamics in the one-dimensional Hubbard model. First, we examine charge, spin, and energy transport away from half-filling and zero magnetization, focusing on the strong coupling regime where we identify a rich interplay of temperature and energy scales, with crossovers between distinct dynamical regimes. We identify an intermediate-temperature regime analogous to the spin-incoherent Lut...

We consider single-particle properties in the one-dimensional repulsive Hubbard model at commensurate fillings in the metallic phase. We determine the real-time evolution of the retarded Green's function by matrix-product state methods. We find that at sufficiently late times the numerical results are in good agreement with predictions of nonlinear Luttinger liquid theory. We argue that combining the two methods provides a way of determining the single-particle spectral funct...

This pre-print deals with the one dimensional Hubbard model, as described by the Pseudofermion Dynamical Theory (PDT), with the purpose of (1) deriving a novel expression for the one electron spectral function for all values of the on-site repulsion $U/t$ and filling $n \in (0,1)$, at vanishing magnetisation $m \rightarrow 0$, and (2) discover how to correctly compare the results originating from two different theoretical frameworks in the $U/t \rightarrow \infty$ limit, as a...

Spin-charge separation (SCS) is a striking manifestation of strong correlations in low-dimensional quantum systems, whereby a fermion splits into separate spin and charge excitations that travel at different speeds. Here, we demonstrate that periodic driving enables control over SCS in a Hubbard system near half-filling. In one dimension, we predict analytically an exotic regime where charge travels slower than spin and can even become 'frozen', in agreement with numerical ca...

In 1968 we published the solution of the ground state energy and wave function of the one-dimensional Hubbard model, and we also showed that there is no Mott transition in this model. Details of the analysis have never been published, however. As the Hubbard model has become increasingly important in condensed matter physics, relating to topics such as the theory of high-T_c superconductivity, it is appropriate to revisit the one-dimensional model and to recall here some deta...

We examine the ground state and excitations of the one dimensional extended Hubbard model with long range interaction. The ground state wavefunctions and low lying excitations are given explicitly in the form of a Jastrow product of two body terms. This results motivates an asymptotic Bethe-ansatz for the model. We present evidence that this solution is in fact exact and spans the complete spectrum of states.

We study the real-time and real-space dynamics of charge in the one-dimensional Hubbard model in the limit of high temperatures. To this end, we prepare pure initial states with sharply peaked density profiles and calculate the time evolution of these nonequilibrium states, by using numerical forward-propagation approaches to chains as long as 20 sites. For a class of typical states, we find excellent agreement with linear-response theory and unveil the existence of remarkabl...