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Physical Review Letters

Collective excitations and spectral function in the Fermi-liquid state of thet-Jmodel

Ziqiang Wang, Yunkyu Bang, Gabriel Kotliar

Published Nov 4, 1991• 38 citations
Publisher

Abstract

We analyze the nature of the single-particle excitations and the collective modes in the nonmagnetic phase of a generalized t-J model to next to leading order in 1/N. We discuss the essential features of the spectral function of the t-J model and we evaluate it numerically for values of the parameters t,J, and of the doping level relevant to the copper-oxide planes.

DOI
10.1103/physrevlett.67.2733

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Physical review. B, Condensed matter•Oct 1, 1994•4 citations
We analyze the nature of the single-particle excitations and the collective modes in the nonmagnetic phase of a generalized t-J model to next to leading order in 1/N. We discuss the essential features of the spectral function of the t-J model and we evaluate it numerically for values of the parameters t,J, and of the doping level relevant to the copper-oxide planes.
New insights into the strongly correlated Fermi liquid state of the SU(N) infinite-U Hubbard and t-J models are presented in connection to the metallic state of unbroken symmetry of the copper oxide planes. The nature of single particle and collective excitations is analyzed and the Landau Fermi Liquid parameters are derived. The one-particle spectral function in the Hubbard valence band is obtained with both Hubbard and Gutzwiller-like features. A simple interpretation of the large incoherent background is given in terms of a superposition of quasiparticles and a collective mode describing the propagation of a bare hole in a large U system. The spin exchange interactions produce very low lying collective modes describing the propagation of staggered spin chirality which soften at incommensurate wavevectors. The quasiparticles are strongly scattered by the low lying chirality fluctuations resulting in deviations from canonical Fermi liquid behavior at low energy scales. Of the same origin, the quasiparticle self energy is found to be strongly k-dependent. It leads to corrections to the dispersion and enhancement of the quasiparticle lifetime in the hole-like region of the interacting Fermi surface. The combined effects are sufficient to produce a sign change in the Hall coefficient evaluated for parameters relevant to the copper oxide planes. We show that these models also exhibit a zero temperature fluctuation driven transition from Fermi liquid to non Fermi liquid phase without the onset of magnetic ordering below a critical doping δc=1/4N, whereby providing a microscopic mechanism for the destruction of the Fermi liquid coherence by strong longitudinal gauge fluctuations which represent the effects of the infinite-U constraint.
Spectral functions within the generalized $t\ensuremath{-}J$ model as relevant to cuprates are analyzed using the method of equations of motion for projected fermion operators. In the evaluation of the self-energy a decoupling of spin and single-particle fluctuations is performed. It is shown that in an undoped antiferromagnet the method reproduces the self-consistent Born approximation. For finite doping with short-range antiferromagnetic order the approximation evolves into a paramagnon contribution which retains a large incoherent contribution in the hole part of the spectral function as well as the hole-pocket-like Fermi surface at low doping. On the other hand, the contribution of longer-range spin fluctuations, with the coupling mostly determined predominantly by J and next-neighbor hopping ${t}^{\ensuremath{'}},$ is essential for the emergence of the pseudogap. The latter shows, at low doping in the effective truncation of the large Fermi surface, a reduced electron density of states and at the same time a quasiparticle density of states at the Fermi level.
We present a nonperturbative method for deriving a quasiparticle description of the low-energy excitations in the t-J model for strongly correlated electrons. Using the exact diagonalization technique we evaluated exactly the spectral functions of composite operators, which describe an electron or hole dressed by antiferromagnetic spin fluctuations as expected in the string or spin bag picture. For hole doping up to 1/8, use of the composite operators leads to a drastic simplification of the single-particle spectral function: at half-filling it takes free-particle form, for the doped case it resembles a system of weakly interacting fermions corresponding to the doped holes. We conclude that for all doping levels studied, the elementary electronic excitations next to the Fermi level are adequately described by the antiferromagnetic spin-fluctuation picture.
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.
Calculations of the one-electron spectral function of the $t\ensuremath{-}J$ model on a two-dimensional square lattice are described. A large-N\mathcal{N}N generalization of the $t\ensuremath{-}J$ model is used to develop 1/N1/\mathcal{N}1/N expansions, and the $t\ensuremath{-}J$ model constraint is enforced by slave bosons. The saddle point about which the 1/N1/\mathcal{N}1/N expansion is carried out is chosen to be uniform in both space and time, and self-energies are calculated to next-to-leading order in 1/N1/\mathcal{N}1/N as in the work of Z. Wang et al. [Phys. Rev. Lett. 67, 2733 (1991)]. The results of computations of the one-electron electron spectral functions for wave vectors throughout the Brillouin zone are presented for several values of the exchange coupling J/tJ/tJ/t and doping $\ensuremath{\delta}$. A sharp dispersive quasiparticle peak is found near the Fermi energy. Additional spectral weight occurs at lower frequencies, and this arises from features in the normal self-energy. These features are qualitatively similar to the self-energy obtained by Kampf and Schrieffer [Phys. Rev. B 41, 6399 (1990)] from a parametrized model of an electron coupled to antiferromagnetic spin fluctuations that leads to shadow band structure in the one-electron spectral function.
Elementary excitations are discussed in the flux-binding phase [Weng, Sheng, and Ting, Phys. Rev. B 49, 607 (1994)] of the t-J model. It is shown that the density and current constraints in the gauge-theory description will dramatically modify the charge excitations. An effective Lagrangian for the normal state of the flux-binding phase is derived, and based on it the transport properties are studied. We find that the resistivity is linearly temperature dependent with a relaxation rate \ensuremath{\Elzxh}/\ensuremath{\tau}\ensuremath{\simeq}2kB{\mathit{k}}_{\mathit{B}}kB​T, and the Hall coefficient involves a second relaxation rate with the cotangent Hall angle following a T2{\mathit{T}}^{2}T2 law. Furthermore, the thermopower exhibits a strong doping dependence. All these features are in good agreement with the transport measurements of the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ copper oxide compounds.