Low energy properties of the metallic state of the two-dimensional t - J model are presented for second neighbor hopping with hole-doping ( ) and electron-doping ( ), with various superexchange energy J . We use a closed set of equations for the Greens functions obtained from the extremely correlated Fermi liquid theory . These equations reproduce the known low energies features of the large U Hubbard model in infinite dimensions. The density and temperature dependent quasiparticle weight, decay rate and the peak spectral heights over the Brillouin zone are calculated. We also calculate the resistivity, Hall conductivity, Hall number and cotangent Hall angle. The spectral features display high thermal sensitivity at modest T for density , implying a suppression of the effective Fermi-liquid temperature by two orders of magnitude relative to the bare bandwidth. The cotangent Hall angle exhibits a T 2 behavior at low T , followed by an interesting kink at higher T . The Hall number exhibits strong renormalization due to correlations. Flipping the sign of changes the curvature of the resistivity versus T curves between convex and concave. Our results provide a natural route for understanding the observed difference in the temperature dependent resistivity of strongly correlated electron-doped and hole-doped matter.
Low energy properties of the metallic state of the two-dimensional t - J model are presented for second neighbor hopping with hole-doping ( ) and electron-doping ( ), with various superexchange energy J . We use a closed set of equations for the Greens functions obtained from the extremely correlated Fermi liquid theory . These equations reproduce the known low energies features of the large U Hubbard model in infinite dimensions. The density and temperature dependent quasiparticle weight, decay rate and the peak spectral heights over the Brillouin zone are calculated. We also calculate the resistivity, Hall conductivity, Hall number and cotangent Hall angle. The spectral features display high thermal sensitivity at modest T for density , implying a suppression of the effective Fermi-liquid temperature by two orders of magnitude relative to the bare bandwidth. The cotangent Hall angle exhibits a T 2 behavior at low T , followed by an interesting kink at higher T . The Hall number exhibits strong renormalization due to correlations. Flipping the sign of changes the curvature of the resistivity versus T curves between convex and concave. Our results provide a natural route for understanding the observed difference in the temperature dependent resistivity of strongly correlated electron-doped and hole-doped matter.
In this work, we apply the extremely correlated Fermi liquid (ECFL) theory into studying the t-t′-J model in one and two dimensions. In 1-d, we combine ECFL and time-dependent density matrix renormalization group (tDMRG) method. The two methods provide a unique insight into the strong momentum dependence of the self-energy of this prototypical non-Fermi liquid, described at low energies as aTomonaga-Luttinger liquid. We also demonstrate its intimate relationship to spin-charge separation,i.e. the splitting of Landau quasiparticles of higher dimensions into two constituents, driven bystrong quantum fluctuations inherent in one dimension. In 2-d, low energy properties of the metallic state of the two-dimensional t-J model are presented for second neighbor hopping with hole-doping (t′leq0) and electron-doping (t′>0), with various superexchange energy J. The density and temperature dependent spectral properties, resistivity and Hall response are calculated. The spectral features display high thermal sensitivity at modest T for density ngeq0.8, implying a suppression of the effective Fermi-liquid temperature by two orders of magnitude relative to the bare bandwidth. Flipping the sign of t′ or varying doping delta changes the curvature of the resistivity versus T curves between convex and concave, consistent to experimental findings.
We study the two-dimensional $t\ensuremath{-}J$ model with second-neighbor hopping parameter ${t}^{\ensuremath{'}}$ and in a broad range of doping $\ensuremath{\delta}$ using a closed set of equations from the extremely correlated Fermi liquid theory. We obtain asymmetric energy distribution curves and symmetric momentum distribution curves of the spectral function, consistent with experimental data. We further explore the Fermi surface and local density of states for different parameter sets. Using the spectral function, we calculate the resistivity, Hall number, and spin susceptibility. The curvature change in the resistivity curves with varying $\ensuremath{\delta}$ is presented and connected to intensity loss in angle-resolved photoemission spectroscopy experiments. We also discuss the role of the superexchange J in the spectral function and the resistivity in the optimal to overdoped density regimes.
We present detailed results from a recent microscopic theory of extremely correlated Fermi liquids, applied to the t-J model in two dimensions, developed recently by Shastry [Phys. Rev. Lett. 107, 056403 (2011); Phys. Rev. B 87, 125124 (2013)]. The second-order theory in the parameter $\ensuremath{\lambda}$, related to the density, is argued to be quantitatively valid in the overdoped regime for $0\ensuremath{\le}n\ensuremath{\lesssim}0.75$, with n denoting the particle density. The calculation involves the self-consistent solution of equations for an auxiliary Fermi liquid Green's function and an adaptive spectral weight. We present numerical results at low as well as high T, at various low to intermediate densities in the normal phase, using a minimal set of band parameters relevant to the cuprate superconductors. We display the momentum space occupation function mk, energy dispersion curves locating the peaks of spectral functions, the optical conductivity, relaxation rates for quasiparticles, and the electronic spectral functions on an absolute scale. The line shapes have an asymmetric shape and a broad background that is also seen in experiments, and our calculations validate approximate recent versions of the theory. The results also display the experimentally noted high-energy kink and provide an in-depth understanding of its origin and dependence on band parameters.
We present the results for the low-energy properties of the infinite-dimensional $t\text{\ensuremath{-}}J$ model with J=0, using $O({\ensuremath{\lambda}}^{2})$ equations of the extremely correlated Fermi liquid formalism. The parameter $\ensuremath{\lambda}\ensuremath{\in}[0,1]$ is analogous to the inverse spin parameter 1/(2S) in quantum magnets. The present analytical scheme allows us to approach the physically most interesting regime near the Mott insulating state $n\ensuremath{\lesssim}1$. It overcomes the limitation to low densities $n\ensuremath{\lesssim}0.7$ of earlier calculations, by employing a variant of the skeleton graph expansion, and a high-frequency cutoff that is essential for maintaining the known high-T entropy. The resulting quasiparticle weight Z, the low $\ensuremath{\omega},T$ self-energy, and the resistivity are reported. These are quite close at all densities to the exact numerical results of the $U=\ensuremath{\infty}$ Hubbard model, obtained using the dynamical mean field theory. The present calculation offers the advantage of generalizing to finite T rather easily, and allows the visualization of the loss of coherence of Fermi liquid quasiparticles by raising T. The present scheme is generalizable to finite dimensions and a nonvanishing J.
Many strongly correlated systems exhibit strange metallic behavior in certain parameter regimes characterized by anomalous transport properties that are irreconcilable with a Fermi-liquid-like description in terms of quasiparticles. The Hubbard model is a standard theoretical starting point to examine the properties of such systems and also exhibits non-Fermi-liquid behavior in simulations. Here we analytically study the two-dimensional hole-doped Hubbard model in the large U limit, first identifying a doping-induced percolation transition in the low-energy sector occurring at a definite critical doping pc depending on lattice structure. Using the critical properties near this transition we rewrite the Hubbard Hamiltonian and motivate a low-energy lattice-independent large-N model with distinct non-Fermi-liquid properties. We show that this model has linear-in-T resistivity with doping-dependent slope maximized at p=pc and power-law optical conductivity ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}2/3}$. Though the parameters used in developing this theory mean it cannot be directly applied to the cuprate superconductors, we nevertheless reproduce several important phenomena observed in their strange metal phase and also predict these same qualitative behaviors to manifest in other lattices near concrete hole dopings.
Abstract Using the strong-coupling diagram technique, low-temperature spectral properties of the two-dimensional fermionic Hubbard model are considered for strong and moderate Hubbard repulsions U . The electron hopping to the nearest, second and third neighbors is taken into account with hopping constants t , t ′ = − 0.3 t and t ″ = 0.2 t , respectively. The nonzero values of t ′ and t ″ lead to strong asymmetry in magnetic properties with respect to the hole and electron doping—for U = 8 t strong antiferromagnetic correlations are retained up to the electron concentration n ¯ ≈ 1.25 , while they are destroyed completely at n ¯ ≈ 0.87 . When the temperature is decreased to T ≲ 0.1 t , in a wide range of electron concentrations there appear narrow and intensive peaks at the Fermi level (FL) in densities of states. For U ≲ 6 t the peaks are seen even at half-filling, while for larger U they arise as the FL leaves the Mott gap. The peaks are connected with a narrow band emerging at low temperatures. We identify states forming the band with spin-polaron excitations—bound states of correlated electrons and mobile spin excitations. Obtained low-temperature spectral functions are used for interpreting the peak-dip-hump structure observed in the photoemission of Nd 2− x Ce x CuO 4 . In the case of hole doping, the calculated Fermi contour contains arcs near nodal points with pseudogaps near antinodal points, while for electron doping the spectral intensity is suppressed at hot spots, in agreement with experimental observations in cuprate perovskites.