Hydrodynamic Formulation of the Hubbard Model

We report results from a systematic analytic strong-coupling expansion of the Bose-Hubbard model in one and two spatial dimensions. We obtain numerically exact results for the dispersion of single particle and single hole excitations in the Mott insulator. The boundary of the Mott phase can be determined with previously unattainable accuracy in one and two dimensions. In one dimension we observe the occurrence of reentrant behavior from the compressible to the insulating phas...

In this Chapter, we present recent theoretical developments on the finite temperature transport of one dimensional electronic and magnetic quantum systems as described by a variety of prototype models. In particular, we discuss the unconventional transport and dynamic - spin, electrical, thermal - properties implied by the integrability of models as the spin-1/2 Heisenberg chain or Hubbard. Furthermore, we address the implication of these developments to experimental studies ...

Using time-dependent density-matrix renormalization group, we study the time evolution of electronic wave packets in the one-dimensional extended Hubbard model with on-site and nearest neighbor repulsion, U and V, respectively. As expected, the wave packets separate into spin-only and charge-only excitations (spin-charge separation). Charge and spin velocities exhibit non-monotonic dependence on V. For small and intermediate values of V, both velocities increase with V. Howev...

It is shown that it is possible to quantitatively explain quantum Monte Carlo results for the Green's function of the two-dimensional Hubbard model in the weak to intermediate coupling regime. The analytic approach includes vertex corrections in a paramagnon-like self-energy. All parameters are determined self-consistently. This approach clearly shows that in two dimensions Fermi-liquid quasiparticles disappear in the paramagnetic state when the antiferromagnetic correlation ...

In this paper we describe the electrons of the 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 $\eta$-spin 1/2 holons, spin 1/2 spinons,...

We investigate finite temperature spin transport in one spatial dimension by considering the spin-spin correlation function of the Hubbard model in the limiting case of infinitely strong repulsion. We find that in the absence of bias the transport is diffusive, and derive the spin diffusion constant. Our approach is based on asymptotic analysis of a Fredholm determinant representation. The obtained results are in agreement with Generalized Hydrodynamics approach.

We investigate the dynamical spin and charge structure factors and the one-particle spectral function of the one-dimensional extended Hubbard model at half band-filling using the dynamical density-matrix renormalization group method. The influence of the model parameters on these frequency- and momentum-resolved dynamical correlation functions is discussed in detail for the Mott-insulating regime. We find quantitative agreement between our numerical results and experiments fo...

Recent developments in the analysis of finite temperature dissipationless transport in integrable quantum many body problems are presented. In particular, we will discuss: (i) the role played by the conservation laws in systems as the spin 1/2 Heisenberg chain and the one-dimensional Hubbard model, (ii) exact results obtained using the Bethe ansatz method on the long time decay of current correlations.

We derive the statistical distribution functions for the Hubbard chain with infinite Coulomb repulsion among particles and for the statistical spin liquid with an arbitrary magnitude of the local interaction in momentum space. Haldane's statistical interaction is derived from an exact solution for each of the two models. In the case of the Hubbard chain the charge (holon) and the spin (spinon) excitations decouple completely and are shown to behave statistically as fermions a...

A self-consistent theory of both spin and charge fluctuations in the Hubbard model is presented. It is in quantitative agreement with Monte Carlo data at least up to intermediate coupling $(U\sim 8t)$. It includes both short-wavelength quantum renormalization effects, and long-wavelength thermal fluctuations which can destroy long-range order in two dimensions. This last effect leads to a small energy scale, as often observed in high temperature superconductors. The theory is...