UC Santa Cruz

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 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. 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 $n\geq 0.8$, 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.