Charge and spin excitations of insulating lamellar copper oxides

A consistent description of low-energy charge and spin responses of the insulating Sr_2CuO_2Cl_2 lamellar system is found in the framework of a one-band Hubbard model which besides $U$ includes hoppings up to 3^{rd} nearest-neighbors. By combining mean-field calculations, exact diagonalization (ED) results, and Quantum Monte Carlo simulations (QMC), we analyze both charge and spin degrees of freedom responses as observed by optical conductivity, ARPES, Raman and inelastic neutron scattering experiments. Within this effective model, long-range hopping processes flatten the quasiparticle band around $(0,\pi)$. We calculate also the non-resonant A_{1g} and B_{1g} Raman profiles and show that the latter is composed by two main features, which are attributed to 2- and 4-magnon scattering.Comment: 6 pages, 3 figures, To be published in PRB (july

Recursion Method in Quantum Spin Dynamics: The Art of Terminating a Continued Fraction

The results obtained from applications of the recursion method to quantum many‐body dynamics can be greatly improved if an appropriate termination function is employed in the continued‐fraction representation of the corresponding relaxation function. We present a general recipe for the construction and use of such termination functions along with two applications in spin dynamics. The method can be adapted to any other problem in quantum many‐body dynamics

Computers from plants we never made. Speculations

We discuss possible designs and prototypes of computing systems that could be based on morphological development of roots, interaction of roots, and analog electrical computation with plants, and plant-derived electronic components. In morphological plant processors data are represented by initial configuration of roots and configurations of sources of attractants and repellents; results of computation are represented by topology of the roots' network. Computation is implemented by the roots following gradients of attractants and repellents, as well as interacting with each other. Problems solvable by plant roots, in principle, include shortest-path, minimum spanning tree, Voronoi diagram, $\alpha$-shapes, convex subdivision of concave polygons. Electrical properties of plants can be modified by loading the plants with functional nanoparticles or coating parts of plants of conductive polymers. Thus, we are in position to make living variable resistors, capacitors, operational amplifiers, multipliers, potentiometers and fixed-function generators. The electrically modified plants can implement summation, integration with respect to time, inversion, multiplication, exponentiation, logarithm, division. Mathematical and engineering problems to be solved can be represented in plant root networks of resistive or reaction elements. Developments in plant-based computing architectures will trigger emergence of a unique community of biologists, electronic engineering and computer scientists working together to produce living electronic devices which future green computers will be made of.Comment: The chapter will be published in "Inspired by Nature. Computing inspired by physics, chemistry and biology. Essays presented to Julian Miller on the occasion of his 60th birthday", Editors: Susan Stepney and Andrew Adamatzky (Springer, 2017

Optical properties of an effective one-band Hubbard model for the cuprates

We study the Cu and O spectral density of states and the optical conductivity of CuO_2 planes using an effective generalized one-band Hubbard model derived from the extended three-band Hubbard model. We solve exactly a square cluster of 10 unit cells and average the results over all possible boundary conditions, what leads to smooth functions of frequency. Upon doping, the Fermi energy jumps to Zhang-Rice states which are connected to the rest of the valence band (in contrast to an isolated new band in the middle of the gap). The transfer of spectral weight depends on the parameters of the original three-band model not only through the one-band effective parameters but also through the relevant matrix elements. We discuss the evolution of the gap upon doping. The optical conductivity of the doped system shows a mid-infrared peak due to intraband transitions, a pseudogap and a high frequency part related to interband transitions. Its shape and integrated weight up to a given frequency (including the Drude weight) agree qualitatively with experiments in the cuprates for low to moderate doping levels, but significant deviations exist for doping $x>0.3$.Comment: 11 pages (tex), 14 figures (ps

Conductivity of CuO3_3-Chains: Disorder versus Electron-Phonon Coupling

The optical conductivity of the CuO$_3$-chains, a subsystem of the 1-2-3 materials, is dominated by a broad peak in the mid-infrared ($\omega \approx 0.2$eV), and a slowly falling high-frequency tail. The 1D $t$-$J$-model is proposed as the relevant low-energy Hamiltonian describing the intrinsic electronic structure of the CuO$_3$-chains. However, due to charge-spin decoupling, this model alone cannot reproduce the observed \sw. We consider two additional scattering mechanisms: (i) Disregarding the not so crucial spin degrees of freedom, the inclusion of strong potential disorder yields excellent agreement with experiment, but suffers from the unreasonable value of the disorder strength necessary for the fit. (ii) Moderately strong polaronic electron-phonon coupling to the mode involving Cu(1)-O(4) stretching, can be modeled within a 1D Holstein Hamiltonian of spinless fermions. Using a variational approximation for the phonon Hilbert space, we diagonalize the Hamiltonian exactly on finite lattices. As a result of the experimental hole density $\approx 1/2$, the chains can exhibit strong charge-density-wave (CDW) correlations, driven by phonon-mediated polaron-polaron interactions. In the vicinity of half filling, charge motion is identified as arising from moving domain walls, \ie defects in the CDW. Incorporating the effect of vacancy disorder by choosing open boundary conditions, good agreement with the experimental spectra is found. In particular, a high-frequency tail arises as a consequence of the polaron-polaron interactions.Comment: 42 pages, ETH-TH/93-31 (Postscript

Kondo resonances and Fano antiresonances in transport through quantum dots

The transmission of electrons through a non-interacting tight-binding chain with an interacting side quantum dot (QD) is analized. When the Kondo effect develops at the dot the conductance presents a wide minimum, reaching zero at the unitary limit. This result is compared to the opposite behaviour found in an embedded QD. Application of a magnetic field destroys the Kondo effect and the conductance shows pairs of dips separated by the charging energy U. The results are discussed in terms of Fano antiresonances and explain qualitatively recent experimental results.Comment: 4 pages including 4 figure

Binding of holes and pair spectral function in the t-J model

Clusters of the two-dimensionnal t--J model with 2 holes and up to 26 sites are diagonalized using a Lanczos algorithm. The behaviour of the binding energy with system size suggests the existence of a finite critical value of J above which binding occurs in the bulk. Only the d-wave pair field operator acting on the Heisenberg GS has a finite overlap with the 2 hole ground state for all the clusters considered. The related spectral function associated with the propagation of a d-wave (spin singlet) pair of holes in the antiferromagnetic background is calculated. The quasiparticle peak at the bottom of the spectrum as well as some structure appearing above the peak survive with increasing cluster size. Although no simple scaling law was found for the quasiparticle weight the data strongly suggest that this weight is finite in the bulk limit and is roughly proportional to the antiferromagnetic coupling J (for J<1).Comment: Report LPQTH-93/01, 18 pages (REVTEX), 8 postscript files include

Melting transition of an Ising glass driven by magnetic field

The quantum critical behavior of the Ising glass in a magnetic field is investigated. We focus on the spin glass to paramagnet transition of the transverse degrees of freedom in the presence of finite longitudinal field. We use two complementary techniques, the Landau theory close to the T=0 transition and the exact diagonalization method for finite systems. This allows us to estimate the size of the critical region and characterize various crossover regimes. An unexpectedly small energy scale on the disordered side of the critical line is found, and its possible relevance to experiments on metallic glasses is briefly discussed.Comment: 4 pages, 3 figure

Correlation Induced Insulator to Metal Transitions

We study a spinless two-band model at half-filling in the limit of infinite dimensions. The ground state of this model in the non-interacting limit is a band-insulator. We identify transitions to a metal and to a charge-Mott insulator, using a combination of analytical, Quantum Monte Carlo, and zero temperature recursion methods. The metallic phase is a non-Fermi liquid state with algebraic local correlation functions with universal exponents over a range of parameters.Comment: 12 pages, REVTE

Density matrix algorithm for the calculation of dynamical properties of low dimensional systems

I extend the scope of the density matrix renormalization group technique developed by White to the calculation of dynamical correlation functions. As an application and performance evaluation I calculate the spin dynamics of the 1D Heisenberg chain.Comment: 4 pages + 4 figures in one Latex + 4 postscript file