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Register a new userFractional Fermi liquid in a generalized $t-J$ model
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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.
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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.
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.
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.
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.
We present numeric results for ground state and angle resolved photoemission spectra (ARPES) for single hole in t-J model coupled to optical phonons. The systematic-error free diagrammatic Monte Carlo is employed where the Feynman graphs for the Matsubara Green function in imaginary time are summed up completely with respect to phonons variables, while magnetic variables are subjected to non-crossing approximation. We obtain that at electron-phonon coupling constants relevant for high Tc cuprates the polaron undergoes self-trapping crossover to strong coupling limit and theoretical ARPES demonstrate features observed in experiment: a broad peak in the bottom of the spectra has momentum dependence which coincides with that of hole in pure t-J model.
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