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Register a new userExtremely Correlated Fermi Liquid theory of the $t$-$J$ model in 2 dimensions: Low Energy properties
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Low energy properties of the metallic state of the 2-dimensional tJ model are presented at various densities and temperatures for second neighbor hopping t, with signs that are negative or positive corresponding to hole or electron doping. The calculation employs a closed set of equations for the Greens functions obtained from the extremely correlated Fermi liquid theory. These equations, when used in $d=infty$ reproduce most of the known low energies features of the $U=infty$ Hubbard model. In 2-dimensions we are able to study the variations due to the superexchange J. The resulting Dyson self energy is found to be momentum dependent as expected. 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 and cotangent of the Hall angle in experimentally relevant units. These display significant thermal sensitivity for density n >~ 0.8, signifying an effective Fermi-liquid temperature scale which is two or three orders of magnitude below the bare bandwidth. Flipping the sign of the hopping t, i.e. studying hole versus electron doping, is found to induce a change in curvature of the temperature dependent resistivity from convex to concave at low temperatures. 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.
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We study the two-dimensional $t$-$J$ model with second neighbor hopping parameter $t$ and in a broad range of doping $delta$ using a closed set of equations from the {em Extremely Correlated Fermi Liquid} (ECFL) 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 $delta$ is presented and connected to intensity loss in Angle Resolved Photoemission Spectroscopy (ARPES) experiments. We also discuss the role of the super-exchange $J$ in the spectral function and the resistivity in the optimal to overdoped density regimes.
We study the one dimensional t-t-J model for generic couplings using two complementary theories, the extremely correlated Fermi liquid theory and time-dependent density matrix renormalization group over a broad energy scale. 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 a Tomonaga-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 by strong quantum fluctuations inherent in one dimension. The momentum distribution function, the spectral function, and the excitation dispersion of these two methods also compare well.
Inspired by the recent discovery of superconductivity in the nickelate Nd$_{1-x}$Sr$_x$NiO$_2$, we study a generalized $t-J$ model to investigate the correlated phases induced by doping spin-one Ni$^{2+}$ into a spin $1/2$ Mott insulator formed by Ni$^{1+}$. Based on a three-fermion parton mean field analysis, we identify a robust fractional Fermi liquid (FL*) phase for almost every doping level. The FL* state is characterized by a small Fermi pocket on top of a spin liquid, which violates the Luttinger theorem of a conventional Fermi liquid and is an example of a symmetric pseudogap metal. Furthermore, we verify our theory in one dimension through density matrix renormalization group (DMRG) simulations on both the generalized $t-J$ model and a two-orbital Hubbard model. The fractional Fermi liquid reduces to fractional Luttinger liquid (LL*) in one dimension, which is connected to the conventional Luttinger liquid through a continuous quantum phase transition by tuning interaction strength. Our findings offer new insights into correlated electron phenomena in nickelate superconductors and other multi-orbital transition metal oxide with spin-triplet $d^8$ state.
We apply the recently developed extremely correlated Fermi liquid theory to the Anderson impurity model, in the extreme correlation limit. We develop an expansion in a parameter lambda, related to n_d, the average occupation of the localized orbital, and find analytic expressions for the Greens functions to O(lambda^2). These yield the impurity spectral function and also the self-energy Sigma(omega) in terms of the two self energies of the ECFL formalism. The imaginary parts of the latter, have roughly symmetric low energy behaviour (~ omega^2), as predicted by Fermi Liquid theory. However, the inferred impurity self energy Sigma(omega) develops asymmetric corrections near n_d ~ 1, leading in turn to a strongly asymmetric impurity spectral function with a skew towards the occupied states. Within this approximation the Friedel sum rule is satisfied but we overestimate the quasiparticle weight z relative to the known exact results, resulting in an over broadening of the Kondo peak. Upon scaling the frequency by the quasiparticle weight z, the spectrum is found to be in reasonable agreement with numerical renormalization group results over a wide range of densities.
We calculate the Landau interaction function f(k,k) for the two-dimensional t-t Hubbard model on the square lattice using second and higher order perturbation theory. Within the Landau-Fermi liquid framework we discuss the behavior of spin and charge susceptibilities as function of the onsite interaction and band filling. In particular we analyze the role of elastic umklapp processes as driving force for the anisotropic reduction of the compressibility on parts of the Fermi surface.
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