Finite-Energy Spectral-Weight Distributions of a 1D Correlated Metal

We derive general closed-form analytical expressions for the finite-energy one- and two-electron spectral-weight distributions of an one-dimensional correlated metal with on-site electronic repulsion. Our results also provide general expressions for the one- and two-atom spectral functions of a correlated quantum system of cold fermionic atoms in a one-dimensional optical lattice with on-site atomic repulsion. In the limit of zero spin density our spectral-function expressions provide the correct zero-spin density results. Our results reveal the dominant non-perturbative microscopic many-particle mechanisms behind the exotic spectral properties observed in quasi-one-dimensional metals and correlated systems of cold fermionic atoms in one-dimensional optical lattices.Comment: 30 pages, no figure

Is the Luttinger liquid a new state of matter?

We are demonstrating that the Luttinger model with short range interaction can be treated as a type of Fermi liquid. In line with the main dogma of Landau's theory one can define a fermion excitation renormalized by interaction and show that in terms of these fermions any excited state of the system is described by free particles. The fermions are a mixture of renormalized right and left electrons. The electric charge and chirality of the Landau quasi-particle is discussed.Comment: paper 10 pages. This version of the paper will be published in Foundations of Physic

Landau theory of phase separation in cuprates

I discuss the problem of phase separation in cuprates from the point of view of the Landau theory of Fermi liquids. I calculate the rate of growth of unstable regions for the hydrodymanics and collisionless limit and, in presence of long range Coulomb interactions, the size of these regions. These are analytic results valid for any strength of the Landau parameters.Comment: RevteX, preprint ITP (1994

Charge and Spin Quantum Fluids Generated by Many-Electron Interactions

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, and $c$ pseudoparticles only. The electronic degrees of freedom couple to external charge (and spin) probes through the holons and $c$ pseudoparticles (and spinons). Our results refer to very large values of the number of lattice sites $N_a$. The holon (and spinon) charge (and spin transport is made by $2\nu$-holon (and $2\nu$-spinon) composite pseudoparticles such that $\nu=1,2,...$.Comment: 25 pages, no figure

The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

The momentum bands, energy dispersions, and velocities of the charge $c$ fermions and spin-neutral two-spinon $s1$ fermions of a square-lattice quantum liquid referring to the Hubbard model on such a lattice of edge length $L$ in the one- and two-electron subspace are studied. The model involves the effective nearest-neighbor integral $t$ and on-site repulsion $U$ and can be experimentally realized in systems of correlated ultra-cold fermionic atoms on an optical lattice and thus our results are of interest for such systems. Our investigations profit from a general rotated-electron description, which is consistent with the model global $SO(3)\times SO(3)\times U(1)$ symmetry. For the model in the one- and two-electron subspace the discrete momentum values of the $c$ and $s1$ fermions are good quantum numbers so that in contrast to the original strongly-correlated electronic problem their interactions are residual. The use of our description renders an involved many-electron problem into a quantum liquid with some similarities with a Fermi liquid.Comment: 61 pages, 1 figure, published in Nuclear Physics

Finite-Temperature Transport in Finite-Size Hubbard Rings in the Strong-Coupling Limit

We study the current, the curvature of levels, and the finite temperature charge stiffness, D(T,L), in the strongly correlated limit, U>>t, for Hubbard rings of L sites, with U the on-site Coulomb repulsion and t the hopping integral. Our study is done for finite-size systems and any band filling. Up to order t we derive our results following two independent approaches, namely, using the solution provided by the Bethe ansatz and the solution provided by an algebraic method, where the electronic operators are represented in a slave-fermion picture. We find that, in the U=\infty case, the finite-temperature charge stiffness is finite for electronic densities, n, smaller than one. These results are essencially those of spinless fermions in a lattice of size L, apart from small corrections coming from a statistical flux, due to the spin degrees of freedom. Up to order t, the Mott-Hubbard gap is \Delta_{MH}=U-4t, and we find that D(T) is finite for n<1, but is zero at half-filling. This result comes from the effective flux felt by the holon excitations, which, due to the presence of doubly occupied sites, is renormalized to \Phi^{eff}=\phi(N_h-N_d)/(N_d+N_h), and which is zero at half-filling, with N_d and N_h being the number of doubly occupied and empty lattice sites, respectively. Further, for half-filling, the current transported by any eigenstate of the system is zero and, therefore, D(T) is also zero.Comment: 15 pages and 6 figures; accepted for PR

Pseudofermion dynamical theory for the spin dynamical correlation functions of the half-filled 1D Hubbard model

A modified version of the metallic-phase pseudofermion dynamical theory (PDT) of the 1D Hubbard model is introduced for the spin dynamical correlation functions of the half-filled 1D Hubbard model Mott– Hubbard phase. The Mott–Hubbard insulator phase PDT is applied to the study of the model longitudinal and transverse spin dynamical structure factors at finite magnetic field h, focusing in particular on the sin- gularities at excitation energies in the vicinity of the lower thresholds. The relation of our theoretical results to both condensed-matter and ultra-cold atom systems is discussed.We thank D.K. Campbell, A. Moreno, and P.D. Sacramento for illuminating discussions and the support by the Beijing CSRC and the FEDER through the COMPETE Program and the Portuguese FCT in the framework of the Strategic Projects PEST-C/FIS/UI0607/2013, PEst-OE/FIS/UI0091/2014, and UID/CTM/04540/2013

One-electron singular spectral features of the 1D Hubbard model at finite magnetic field

The momentum, electronic density, spin density, and interaction dependences of the exponents that con-trol the (k, ω)-plane singular features of the σ=↑, ↓one-electron spectral functions of the 1D Hubbard model at finite magnetic field are studied. The usual half-filling concepts of one-electron lower Hubbard band and upper Hubbard band are defined in terms of the rotated electrons associated with the model Bethe-ansatz solution for all electronic density and spin density values and the whole finite repulsion range. Such rotated electrons are the link of the non-perturbative relation between the electrons and the pseudofermions. Our results further clarify the microscopic processes through which the pseudofermion dynamical theory accounts for the one-electron matrix elements between the ground state and excited energy eigenstates.Portuguese FCT through the Grant UID/FIS/04650/2013info:eu-repo/semantics/publishedVersio

Absence of ballistic charge transport in the half-filled 1D Hubbard model

Whether in the thermodynamic limit of lattice length infinite, hole concentration tending to zero, nonzero temperature, and U/t > 0 the charge stiffness of the 1D Hubbard model with first neighbor transfer integral t and on-site repulsion U is finite or vanishes and thus whether there is or there is no ballistic charge transport, respectively, remains an unsolved and controversial issue, as different approaches yield contradictory results. In this paper we provide an upper bound on the charge stiffness and show that (similarly as at zero temperature), for T >0 and U/t>0 it vanishes in the limit of zero hole concentration within the canonical ensemble in the thermodynamic limit. Moreover, we show that at high temperature the charge stiffness vanishes as well within the grand-canonical ensemble in the infinite lattice length limit and chemical potential approaching half the Mott-Hubbard gap. The lack of charge ballistic transport indicates that charge transport at finite temperatures is dominated by a diffusive contribution. Our scheme uses a suitable exact representation of the electrons in terms of rotated electrons for which the numbers of singly occupied and doubly occupied lattice sites are good quantum numbers for U/t>0. In contrast to often less controllable numerical studies, the use of such a representation reveals the carriers that couple to the charge probes and provides useful physical information on the microscopic processes behind the exotic charge transport properties of the 1D electronic correlated system under study.We thank David K. Campbell, Pedro D. Sacramento, and Xenophon Zotos for discussions. J. M. P. C. and S. N. thank the support from C. S. R. C. (Beijing) and J. M. P. C. and T. P. acknowledge the support of the ERC Advanced Grant 694544 - OMNES. J. M. P. C. thanks the support by the Portuguese FCT through the Grant UID/FIS/04650/2013. T. P. acknowledges the support from the Grants of the Slovenian Research Agency (ARRS) P1-004 and N1-0025

Absence of high-temperature ballistic transport in the spin-1/2 XXX chain within the grand-canonical ensemble

Whether in the thermodynamic limit, vanishing magnetic field h →0, and nonzero temperature the spin stiffness of the spin-1/2XXXHeisenberg chain is finite or vanishes within the grand-canonical ensemble remains an unsolved and controversial issue, as different approaches yield contradictory results. Here we provide an upper bound on the stiffness and show that within that ensemble it vanishes for h →0in the thermodynamic limit of chain length L →∞, at high temperatures T→∞. Our approach uses a represen-tation in terms of the Lphysical spins 1/2. For all configurations that generate the exact spin-Senergy and momentum eigenstates such a configuration involves a number 2Sof unpaired spins 1/2in multiplet con-figurations and L −2Sspins 1/2that are paired within Msp=L/2 −Sspin–singlet pairs. The Bethe-ansatz strings of length n =1and n >1describe a single unbound spin–singlet pair and a configuration within which npairs are bound, respectively. In the case of n >1pairs this holds both for ideal and deformed strings associated with ncomplex rapidities with the same real part. The use of such a spin 1/2repre-sentation provides useful physical information on the problem under investigation in contrast to often less controllable numerical studies. Our results provide strong evidence for the absence of ballistic transport in the spin-1/2XXXHeisenberg chain in the thermodynamic limit, for high temperatures T→∞, vanishing magnetic field h →0and within the grand-canonical ensemble.We thank David K. Campbell, Pedro. D. Sacramento, and Xenophon Zotos for discussions. J.M.P.C. thanks the support by the Portuguese FCT through the Grant UID/FIS/04650/2013. T.P. acknowledges support by the Grants of Slovenian Research Agency (ARRS) P1-0044, N1-0025, and J1-5439.info:eu-repo/semantics/publishedVersio