The Hall coefficient in the strongly correlated Fermi-liquid phase of the t-J model is studied for moderate hole concentrations. We find that the quasiparticle self-energy is strongly k dependent due to gauge-field interactions. It leads to corrections to the Fermi-surface curvature and to enhancement of the quasiparticle lifetime in the holelike region. We show that a systematic treatment of the strong local correlations to next to leading order in 1/N is sufficient to give rise to a sign change in the Hall coefficient. This effect occurs near 0.20 doping for J/t=0.2 and may be relevant to the high-
Tc materials.
It has long since been argued that the metallic states of the single-band Hubbard Hamiltonian Ĥ in two spatial dimensions (i.e. for d = 2) should be non-Fermi liquid, a possibility that would lead to the understanding of the observed anomalous behaviour of the doped copper-oxide-based superconducting compounds in their normal metallic states. Here we present a formalism which enables us to express, for arbitrary d, the behaviour of the momentum-distribution function nσ(k) pertaining to uniform metallic ground states of Ĥ close to S F; σ (the Fermi surface of the fermions with spin index σ, σ = ↑, ↓) in terms of a small number of constant parameters which are bound to satisfy certain inequalities implied by the requirement of the stability of the ground state of the system. These inequalities restrict the range of variation in nσ(k) for k infinitesimally inside and outside the Fermi sea pertaining to fermions with spin index σ and consequently the range of variation in the zero-temperature limit of nσ(k) for k on S F; σ On the basis of some available accurate numerical results for nσ(k) pertaining to the Hubbard and the t-J Hamiltonian, we conclude that, at least in the strong-coupling regime, the metallic ground states of Ĥ for d = 2 cannot be Fermi-liquid nor can they in general be purely Luttinger or marginal Fermi liquids. We further rigorously identify the pseudogap phenomenon, or 'truncation' of the Fermi surface, clearly observed in the normal states of underdoped copper-oxide-based superconductors, as corresponding to a line of resonance energies (i.e. these energies strictly do not relate to quasiparticles) located below the Fermi energy, with a concomitant suppression to zero of the jump in nσ(k) over the 'truncated' parts of the Fermi surface. Our analyses make explicit the singular significance of the non-interacting energy dispersion ε k underlying Ĥ in determining the low-energy spectral and transport properties of the metallic ground states of Ĥ.
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.
In this paper, we present a theoretical framework for understanding the extremely correlated Fermi liquid (ECFL) phenomenon within the $U=\ensuremath{\infty}$ Hubbard model. Our approach involves deriving equations of motion for the single-particle Green's function
G and its associated self-energy $\mathrm{\ensuremath{\Sigma}}$, which involves the product of the bosonic correlation function comprising both density
(DN) and spin
(DS) correlations with
G. By solving these equations self-consistently, we explore the behavior of
G,
DN, and
DS as functions of frequency, temperature, and hole concentration. Our results reveal distinct coherent and incoherent Fermi liquid regimes characterized by the presence or absence of quasiparticle excitations. Additionally, we analyze the intrinsic dc resistivity $\ensuremath{\rho}(T)$, observing a crossover from
T2 to linear behavior with increasing temperature. Our findings delineate Fermi liquid, quantum incoherent, and ``classical'' regimes in strongly correlated systems, emphasizing the importance of quantum diffusive local charge and spin fluctuations.