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arXiv:1808.09788 · Physical review. B./Physical review. B

Extremely correlated Fermi liquid of the t−J model in two dimensions

Peizhi Mai, B. Sriram Shastry

Published Nov 5, 2018• 10 citations
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Abstract

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.

DOI
10.1103/physrevb.98.205106

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We study the two-dimensional t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model with second-neighbor hopping parameter t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′ and in a broad range of doping \ensuremathδ\ensuremath{\delta}\ensuremathδ 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 \ensuremathδ\ensuremath{\delta}\ensuremathδ is presented and connected to intensity loss in angle-resolved photoemission spectroscopy experiments. We also discuss the role of the superexchange JJJ in the spectral function and the resistivity in the optimal to overdoped density regimes.
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 ttt-t′t't′-JJJ 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 ttt-JJJ model are presented for second neighbor hopping with hole-doping (t′leq0t'\\leq0t′leq0) and electron-doping (t′>0t'>0t′>0), with various superexchange energy JJJ. 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 ngeq0.8n\\geq 0.8ngeq0.8, implying a suppression of the effective Fermi-liquid temperature by two orders of magnitude relative to the bare bandwidth. Flipping the sign of t′t't′ or varying doping delta\\deltadelta changes the curvature of the resistivity versus T curves between convex and concave, consistent to experimental findings.
We present detailed results from a recent microscopic theory of extremely correlated Fermi liquids, applied to the ttt-JJJ 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 nnn 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 TTT, 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{m}_{k}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.
Using a recently developed perturbative approach, which considers Hubbard operators as fundamental excitations, we have performed electronic self-energy and spectral function calculations for the $t\text{\ensuremath{-}}J$ model on the square lattice. We have found that the spectral functions along the Fermi surface are isotropic, even close to the critical doping where the ddd density wave phase occurs. Fermi liquid behavior with scattering rate $\ensuremath{\sim}{\ensuremath{\omega}}^{2}$ and a finite quasiparticle weight ZZZ was obtained. ZZZ decreases with decreasing doping taking low values for low doping. Results are compared with others obtained by analytical and numerical methods like the slave-boson and Lanczos diagonalization approaches, finding agreement. We discuss our results in the light of recent angle-resolved photoemission spectroscopy experiments in cuprates.
We present an exact diagonalization study of the self-energy of the two-dimensional Hubbard model. To increase the range of available cluster sizes we use a corrected ttt-JJJ model to compute approximate Green's functions for the Hubbard model. This allows to obtain spectra for clusters with 18 and 20 sites. The self-energy has several ``bands'' of poles with strong dispersion and extended incoherent continua with kkk-dependent intensity. We fit the self-energy by a minimal model and use this to extrapolate the cluster results to the infinite lattice. The resulting Fermi surface shows a transition from hole pockets in the underdoped regime to a large Fermi surface in the overdoped regime. We demonstrate that hole pockets can be completely consistent with the Luttinger theorem. Introduction of next-nearest-neighbor hopping changes the self-energy strongly and the spectral function with nonvanishing next-nearest-neighbor hopping in the underdoped region is in good agreement with angle-resolved photoelectron spectroscopy in the cuprates.
We present the results for the low-energy properties of the infinite-dimensional $t\text{\ensuremath{-}}J$ model with J=0J=0J=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)1/(2S)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-TTT entropy. The resulting quasiparticle weight ZZZ, 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 TTT rather easily, and allows the visualization of the loss of coherence of Fermi liquid quasiparticles by raising TTT. The present scheme is generalizable to finite dimensions and a nonvanishing JJJ.