Lattice susceptibility for 2D Hubbard Model within dual fermion method

In this paper, we present details of the dual fermion (DF) method to study the non-local correction to single site DMFT. The DMFT two-particle Green's function is calculated using continuous time quantum monte carlo (CT-QMC) method. The momentum dependence of the vertex function is analyzed and its renormalization based on the Bethe-Salpeter equation is performed in particle-hole channel. We found a magnetic instability in both the dual and the lattice fermions. The lattice fermion susceptibility is calculated at finite temperature in this method and also in another recently proposed method, namely dynamical vertex approximation (D$\Gamma$A). The comparison between these two methods are presented in both weak and strong coupling region. Compared to the susceptibility from quantum monte carlo (QMC) simulation, both of them gave satisfied results.Comment: 10 pages, 11 figure

Spin-charge separation in ultra-cold quantum gases

We investigate the physical properties of quasi-1D quantum gases of fermion atoms confined in harmonic traps. Using the fact that for a homogeneous gas, the low energy properties are exactly described by a Luttinger model, we analyze the nature and manifestations of the spin-charge separation. Finally we discuss the necessary physical conditions and experimental limitations confronting possible experimental implementations.Comment: 4 pages, revtex4, 2 eps figure

Bounded Counter Languages

We show that deterministic finite automata equipped with $k$ two-way heads are equivalent to deterministic machines with a single two-way input head and $k-1$ linearly bounded counters if the accepted language is strictly bounded, i.e., a subset of $a_1^*a_2^*... a_m^*$ for a fixed sequence of symbols $a_1, a_2,..., a_m$. Then we investigate linear speed-up for counter machines. Lower and upper time bounds for concrete recognition problems are shown, implying that in general linear speed-up does not hold for counter machines. For bounded languages we develop a technique for speeding up computations by any constant factor at the expense of adding a fixed number of counters

Charge transfer fluctuation, d−d-wave superconductivity, and the B1gB_{1g} Raman phonon in the Cuprates: A detailed analysis

The Raman spectrum of the $B_{1g}$ phonon in the superconducting cuprate materials is investigated theoretically in detail in both the normal and superconducting phases, and is contrasted with that of the $A_{1g}$ phonon. A mechanism involving the charge transfer fluctuation between the two oxygen ions in the CuO$_2$ plane coupled to the crystal field perpendicular to the plane is discussed and the resulting electron-phonon coupling is evaluated. Depending on the symmetry of the phonon the weight of different parts of the Fermi surface in the coupling is different. This provides the opportunity to obtain information on the superconducting gap function at certain parts of the Fermi surface. The lineshape of the phonon is then analyzed in detail both in the normal and superconducting states. The Fano lineshape is calculated in the normal state and the change of the linewidth with temperature below T$_{c}$ is investigated for a $d_{x^{2}-y^{2}}$ pairing symmetry. Excellent agreement is obtained for the $B_{1g}$ phonon lineshape in YBa$_{2}$Cu$_{3}$O$_{7}$. These experiments, however, can not distinguish between $d_{x^{2}-y^{2}}$ and a highly anisotropic $s$-wave pairing.Comment: Revtex, 21 pages + 4 postscript figures appended, tp

Line-distortion, Bandwidth and Path-length of a graph

We investigate the minimum line-distortion and the minimum bandwidth problems on unweighted graphs and their relations with the minimum length of a Robertson-Seymour's path-decomposition. The length of a path-decomposition of a graph is the largest diameter of a bag in the decomposition. The path-length of a graph is the minimum length over all its path-decompositions. In particular, we show: - if a graph $G$ can be embedded into the line with distortion $k$, then $G$ admits a Robertson-Seymour's path-decomposition with bags of diameter at most $k$ in $G$; - for every class of graphs with path-length bounded by a constant, there exist an efficient constant-factor approximation algorithm for the minimum line-distortion problem and an efficient constant-factor approximation algorithm for the minimum bandwidth problem; - there is an efficient 2-approximation algorithm for computing the path-length of an arbitrary graph; - AT-free graphs and some intersection families of graphs have path-length at most 2; - for AT-free graphs, there exist a linear time 8-approximation algorithm for the minimum line-distortion problem and a linear time 4-approximation algorithm for the minimum bandwidth problem

NMR and Neutron Scattering Experiments on the Cuprate Superconductors: A Critical Re-Examination

We show that it is possible to reconcile NMR and neutron scattering experiments on both LSCO and YBCO, by making use of the Millis-Monien-Pines mean field phenomenological expression for the dynamic spin-spin response function, and reexamining the standard Shastry-Mila-Rice hyperfine Hamiltonian for NMR experiments. The recent neutron scattering results of Aeppli et al on LSCO (x=14%) are shown to agree quantitatively with the NMR measurements of $^{63}T_1$ and the magnetic scaling behavior proposed by Barzykin and Pines. The reconciliation of the $^{17}T_1$ relaxation rates with the degree of incommensuration in the spin fluctuation spectrum seen in neutron experiments is achieved by introducing a new transferred hyperfine coupling $C'$ between oxygen nuclei and their next nearest neighbor $Cu^{2+}$ spins; this leads to a near-perfect cancellation of the influence of the incommensurate spin fluctuation peaks on the oxygen relaxation rates of LSCO. The inclusion of the new $C'$ term also leads to a natural explanation, within the one-component model, the different temperature dependence of the anisotropic oxygen relaxation rates for different field orientations, recently observed by Martindale $et~al$. The measured significant decrease with doping of the anisotropy ratio, $R= ^{63}T_{1ab}/^{63}T_{1c}$ in LSCO system, from $R =3.9$ for ${\rm La_2CuO_4}$ to $R ~ 3.0$ for LSCO (x=15%) is made compatible with the doping dependence of the shift in the incommensurate spin fluctuation peaks measured in neutron experiments, by suitable choices of the direct and transferred hyperfine coupling constants $A_{\beta}$ and B.Comment: 24 pages in RevTex, 9 figures include

Resistivity as a function of temperature for models with hot spots on the Fermi surface.

We calculate the resistivity $\rho$ as a function of temperature $T$ for two models currently discussed in connection with high temperature superconductivity: nearly antiferromagnetic Fermi liquids and models with van Hove singularities on the Fermi surface. The resistivity is calculated semiclassicaly by making use of a Boltzmann equation which is formulated as a variational problem. For the model of nearly antiferromagnetic Fermi liquids we construct a better variational solution compared to the standard one and we find a new energy scale for the crossover to the $\rho\propto T^2$ behavior at low temperatures. This energy scale is finite even when the spin-fluctuations are assumed to be critical. The effect of additional impurity scattering is discussed. For the model with van Hove singularities a standard ansatz for the Boltzmann equation is sufficient to show that although the quasiparticle lifetime is anomalously short, the resistivity $\rho\propto T^2\ln(1/T)$.Comment: Revtex 3.0, 8 pages; figures available upon request. Submitted to Phys. Rev. B

Quasiparticle spectrum in a nearly antiferromagnetic Fermi liquid: shadow and flat bands

We consider a two-dimensional Fermi liquid in the vicinity of a spin-density-wave transition to a phase with commensurate antiferromagnetic long-range order. We assume that near the transition, the Fermi surface is large and crosses the magnetic Brillouin zone boundary. We show that under these conditions, the self-energy corrections to the dynamical spin susceptibility, $\chi (q, \omega)$, and to the quasiparticle spectral function function, $A(k, \omega)$, are divergent near the transition. We identify and sum the series of most singular diagrams, and obtain a solution for $\chi(q, \omega)$ and an approximate solution for $A(k, \omega)$. We show that (i) $A(k)$ at a given, small $\omega$ has an extra peak at $k = k_F + \pi$ (`shadow band'), and (ii) the dispersion near the crossing points is much flatter than for free electrons. The relevance of these results to recent photoemission experiments in $YBCO$ and $Bi2212$ systems is discussed.Comment: a sign and amplitude of the vertex renormalization and few typos are correcte

On rr-Simple kk-Path

An $r$-simple $k$-path is a {path} in the graph of length $k$ that passes through each vertex at most $r$ times. The $r$-SIMPLE $k$-PATH problem, given a graph $G$ as input, asks whether there exists an $r$-simple $k$-path in $G$. We first show that this problem is NP-Complete. We then show that there is a graph $G$ that contains an $r$-simple $k$-path and no simple path of length greater than $4\log k/\log r$. So this, in a sense, motivates this problem especially when one's goal is to find a short path that visits many vertices in the graph while bounding the number of visits at each vertex. We then give a randomized algorithm that runs in time $$\mathrm{poly}(n)\cdot 2^{O( k\cdot \log r/r)}$$ that solves the $r$-SIMPLE $k$-PATH on a graph with $n$ vertices with one-sided error. We also show that a randomized algorithm with running time $\mathrm{poly}(n)\cdot 2^{(c/2)k/ r}$ with $c<1$ gives a randomized algorithm with running time \poly(n)\cdot 2^{cn} for the Hamiltonian path problem in a directed graph - an outstanding open problem. So in a sense our algorithm is optimal up to an $O(\log r)$ factor