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arXiv:cond-mat/9412116 · Physical review. B, Condensed matter

Charge dynamics in the planart-Jmodel

Janez Jaklič, Peter Prelovšek

Published Sep 1, 1995• 37 citations
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Abstract

The finite-temperature optical conductivity \ensuremath{\sigma}(\ensuremath{\omega}) in the planar t-J model is analyzed using recently introduced numerical method based on the Lanczos diagonalization of small systems (up to 20 sites), as well as by analytical approaches, including the method of frequency moments and the retraceable-path approximation. Results for a dynamical mobility of a single hole at elevated temperatures T>t reveal a Gaussian-like \ensuremath{\mu}(\ensuremath{\omega}) spectra, however, with a nonanalytical behavior at low \ensuremath{\omega}. In the single-hole response a difference between the ferromagnetic (J=0) and the antiferromagnetic (J>0) polaron shows up at TJ. At larger dopings numerical results in studied systems are consistent with the thermodynamical behavior for T>${\mathit{T}}^{\mathrm{*}}$\ensuremath{\ge}0.1t. $sigma ( omega )--- spectra show a non-Drude falloff at large frequencies. In particular for ``optimum'' doping ${\mathit{n}}_{\mathit{h}}$\ensuremath{\sim}0.2 we obtain in the low-\ensuremath{\omega},T regime the relaxation rate ${\mathrm{\ensuremath{\tau}}}^{\mathrm{\ensuremath{-}}1}$\ensuremath{\sim}2\ensuremath{\pi}\ensuremath{\lambda}(\ensuremath{\omega}+\ensuremath{\xi}T) with \ensuremath{\lambda}\ensuremath{\sim}0.09 and \ensuremath{\xi}\ensuremath{\sim}2.7, being consistent with the marginal Fermi-liquid concept and experiments. Within the same regime we reproduce the nearly linear variation of dc resistivity \ensuremath{\rho} with T. This behavior is weakly dependent on J, provided that Jt.

DOI
10.1103/physrevb.52.6903

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The finite-temperature optical conductivity \ensuremath{\sigma}(\ensuremath{\omega}) in the planar t-J model is analyzed using recently introduced numerical method based on the Lanczos diagonalization of small systems (up to 20 sites), as well as by analytical approaches, including the method of frequency moments and the retraceable-path approximation. Results for a dynamical mobility of a single hole at elevated temperatures T>t reveal a Gaussian-like \ensuremath{\mu}(\ensuremath{\omega}) spectra, however, with a nonanalytical behavior at low \ensuremath{\omega}. In the single-hole response a difference between the ferromagnetic (J=0) and the antiferromagnetic (J>0) polaron shows up at TJ. At larger dopings numerical results in studied systems are consistent with the thermodynamical behavior for T>T∗{\mathit{T}}^{\mathrm{*}}T∗\ensuremath{\ge}0.1t. sigma(omega)−−−spectrashowanon−Drudefalloffatlargefrequencies.Inparticularfor‘‘optimum′′dopingsigma ( omega )--- spectra show a non-Drude falloff at large frequencies. In particular for ``optimum'' doping sigma(omega)−−−spectrashowanon−Drudefalloffatlargefrequencies.Inparticularfor‘‘optimum′′doping{\mathit{n}}_{\mathit{h}}\ensuremath∼0.2weobtaininthelow−\ensuremathω,Tregimetherelaxationrate\ensuremath{\sim}0.2 we obtain in the low-\ensuremath{\omega},T regime the relaxation rate \ensuremath∼0.2weobtaininthelow−\ensuremathω,Tregimetherelaxationrate{\mathrm{\ensuremath{\tau}}}^{\mathrm{\ensuremath{-}}1}$\ensuremath{\sim}2\ensuremath{\pi}\ensuremath{\lambda}(\ensuremath{\omega}+\ensuremath{\xi}T) with \ensuremath{\lambda}\ensuremath{\sim}0.09 and \ensuremath{\xi}\ensuremath{\sim}2.7, being consistent with the marginal Fermi-liquid concept and experiments. Within the same regime we reproduce the nearly linear variation of dc resistivity \ensuremath{\rho} with T. This behavior is weakly dependent on J, provided that Jt.
Results are for finite-temperature optical conductivity \ensuremath{\sigma}(\ensuremath{\omega}) and dc resistivity \ensuremath{\rho}(T), obtained within the t-J model on a square lattice by a method based on the Lanczos diagonalization. Studying systems with N=16 or 18 sites and hole concentrations ch{\mathit{c}}_{\mathit{h}}ch​\ensuremath{\le}0.25, a thermodynamic behavior is reached for quite low temperatures. \ensuremath{\sigma}(\ensuremath{\omega}) spectra reveal a slow non-Drude falloff at large frequencies and the emergence of a broad midinfrared peak at low doping. At optimum doping \ensuremath{\rho}(T) shows nearly linear variation with T. Both quantities agree well with experimental results in cuprates.
We calculate the optical conductivity \ensuremath{\sigma}(\ensuremath{\omega}) of the Hubbard and t-J models on 10- and 16-site lattices, respectively, using a Lanczos method. Results are presented for various values of the couplings U/t, J/t, and band fillings, using free- and periodic-boundary conditions. We discuss the behavior of the kinetic energy in the ground state, the distribution of spectral weight of \ensuremath{\sigma}(\ensuremath{\omega}) between low and high energies and the sum rule. Indications of a Drude-like peak at low energy in the one-hole subspace are observed in both models. Assuming that holes behave like independent (mass-renormalized) particles in the normal state of the superconductors, our results also suggest that the optical midinfrared broadband observed experimentally can be explained by hole excitations of strongly correlated systems.
The dynamic charge susceptibility and the optical conductivity are calculated in the planar $t\ensuremath{-}J$ model within the memory function method, working directly in terms of Hubbard operators. The density fluctuation spectrum consists of a damped soundlike mode for small wave vectors and a broad high energy peak $(\ensuremath{\sim}t)$ for large momenta. The study of the optical conductivity shows that electron scattering from spin fluctuations leads to the Drude-frequency dependent relaxation rate which exhibits a crossover from ${\ensuremath{\omega}}^{3/2}$ behavior at low frequencies $(\ensuremath{\omega}<2|\ensuremath{\mu}|),$ to a linear $\ensuremath{\omega}$ dependence for frequencies larger than $2|\ensuremath{\mu}|.$ Due to the spin-polaron nature of charge carriers, extra absorptions arise starting at a frequency $\ensuremath{\omega}\ensuremath{\gtrsim}J.$ The obtained results are in a good agreement with exact diagonalization studies.
The single-particle spectral functions A(k,\ensuremath{\omega}) and self-energies \ensuremath{\Sigma}(k,\ensuremath{\omega}) are calculated within the t-J model using the finite-temperature Lanczos method for small systems. A remarkable asymmetry between the electron and hole part is found. The hole (photoemission) spectra are overdamped, with Im\ensuremath{\Sigma}\ensuremath{\propto}\ensuremath{\omega} in a wide energy range, consistent with the marginal Fermi liquid scenario, and in good agreement with experiments on cuprates. In contrast, the quasiparticles in the electron part of the spectrum show weak damping.
The spin-diffusion constant of the two-dimensional t-J model is calculated using an analytical approach at high temperatures and a recently developed numerical method based on the Lanczos technique combined with random sampling in the intermediate temperature regime. A simple relation, \ensuremath{\sigma}=Ds{\mathit{D}}_{\mathit{s}}Ds​\ensuremath{\chi}, between spin conductivity and spin diffusion is established and used to calculate the latter. In the high-temperature and low-doping limit, the calculated diffusion constant agrees with known results for the Heisenberg model. At small hole doping, Ds{\mathit{D}}_{\mathit{s}}Ds​ increases approximately linearly with doping, which leads us to an important conclusion that hopping processes enhance spin diffusion at high temperatures. At modest hole doping, \ensuremath{\delta}\ensuremath{\sim}0.25, diffusion exhibits a nonmonotonic temperature dependence, which indicates anomalous spin dynamics at small frequencies.
Recent results for the finite-temperature static and dynamical properties of the planar t−Jt-Jt−J model, obtained by a novel numerical method for small correlated systems, are reviewed. Of particular interest are T>0T>0T>0 charge and spin response functions: optical conductivity σ(ω)σ(ω)σ(ω) and spin susceptibility χ(q⃗,ω)χ(\vec q,ω)χ(q​,ω), which show very universal features at intermediate doping. In spin dynamics the universality is best seen in the local spin correlation function, which appears to be TTT-independent and only weakly doping dependent. Results apply directly to the inelastic neutron scattering and to the NMR relaxation experiments in cuprates. Analysing σ(ω)σ(ω)σ(ω) we find that the current correlation function C(ω)C(ω)C(ω) is nearly TTT- and moreover ωωω-independent in the regime $T