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arXiv:cond-mat/9601073

Universality of Charge and Spin Response in Doped Antiferromagnets

Peter Prelovšek, Janez Jaklič

Published Jan 18, 1996• 0 citations
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Abstract

Recent results for the finite-temperature static and dynamical properties of the planar $t-J$ model, obtained by a novel numerical method for small correlated systems, are reviewed. Of particular interest are $T>0$ charge and spin response functions: optical conductivity $σ(ω)$ and spin susceptibility $χ(\vec q,ω)$, 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 $T$-independent and only weakly doping dependent. Results apply directly to the inelastic neutron scattering and to the NMR relaxation experiments in cuprates. Analysing $σ(ω)$ we find that the current correlation function $C(ω)$ is nearly $T$- and moreover $ω$-independent in the regime $T

DOI
10.48550/arxiv.cond-mat/9601073

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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
We review recent results for the properties of doped antiferromagnets, obtained by the numerical analysis of the planar t-J model using the novel finite-temperature Lanczos method for small correlated systems. First we briefly summarize our present understanding of anomalous normal-state properties of cuprates, and present the electronic phase diagram, phenomenological scenarios and models proposed in this connection. The numerical method is then described in more detail. The following sections are devoted to various static and dynamical properties of the t-J model. Among the thermodynamic properties the chemical potential, entropy and the specific heat are evaluated. Discussing electrical properties the emphasis is on the planar optical conductivity and the d.c. resistivity. Magnetic properties involve the static and dynamical spin structure factor, as measured via the susceptibility measurements, the NMR relaxation and the neutron scattering, as well as the orbital current contribution. The analysis of electron spectral functions, studied by photoemission experiments, and their relation to the c-axis conductivity, follows. Finally we discuss density fluctuations, the electronic Raman scattering and the thermoelectric power. Whenever feasible a comparison with experimental data is performed. A general conclusion is that the t-J model captures well the main features of anomalous normal-state properties of cuprates, for a number of quantities the agreement is even a quantitative one. It is shown that several dynamical quantities exhibit at intermediate doping a novel universal behaviour consistent with a marginal Fermi-liquid concept, which seems to emerge from a large degeneracy of states and a frustration induced by doping the antiferro magnet.
Charge and spin response in the planar $t\ensuremath{-}J$ model at finite temperatures are investigated numerically, in the regime corresponding to cuprates at intermediate doping. We show that the local spin correlation function is TTT independent, leading to ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}(\ensuremath{\omega}<J)\ensuremath{\propto}\mathrm{tanh}(\ensuremath{\omega}/2T)$. The current correlation function $C(\ensuremath{\omega})$ appears to be TTT as well as $\ensuremath{\omega}$ independent, and the optical conductivity $\ensuremath{\sigma}\ensuremath{\propto}({1\ensuremath{-}e}^{\ensuremath{-}\ensuremath{\omega}/T})/\ensuremath{\omega}$. Such anomalous response functions are brought in connection with the large entropy persisting at T<JT<JT<J.
Finite-temperature spin dynamics in the planar $t\ensuremath{-}J$ model are studied using a method based on the Lanczos diagonalization of small systems. The dynamical spin structure factor at moderate dopings shows the coexistence of free-fermion-like and spin-fluctuation time scales. At T<JT<JT<J, low-frequency and static susceptibilities show a pronounced TTT dependence, supporting a scenario related to the marginal Fermi liquid one, for the explanation of neutron-scattering and NMR relaxation experiments in cuprates. Calculated NMR relaxation rates reasonably reproduce experimental ones.
We investigate the dynamical charge-charge correlation function and the optical conductivity in weakly doped antiferromagnets using Mori-Zwanzig projection technique. The system is described by the two-dimensional t - J model. The arising matrix elements are evaluated within a cumulant formalism which was recently applied to investigate magnetic properties of weakly doped antiferromagnets. Within the present approach the ground state consists of non-interacting hole quasiparticles. Our spectra agree well with numerical results calculated via exact diagonalization techniques. The method we employ enables us to explain the features present in the correlation functions. We conclude that the charge dynamics at weak doping is governed by transitions between excited states of spin-bag quasiparticles.
Using high temperature expansions for the equal time correlator S(q) and static susceptibility \ensuremath{\chi}(q) for the t-J model, we present evidence for quantum critical (QC), z=1, behavior at intermediate temperature in a broad range of t/J ratio, doping, and temperatures. We find that the dynamical susceptibility is very close to the universal scaling function computable for the asymptotic QC regime, and that the dominant energy scale is temperature. Our results are in excellent agreement with measurements of the spin-echo decay rate, 1/T2G{\mathit{T}}_{2\mathrm{G}}T2G​, in La2{\mathrm{La}}_{2}La2​CuO4{\mathrm{CuO}}_{4}CuO4​, and provide qualitative understanding of both 1/T1{\mathit{T}}_{1}T1​ and 1/T2G{\mathit{T}}_{2\mathrm{G}}T2G​ nuclear relaxation rates in doped cuprates.
A real spin-charge separation scheme is found based on a saddle-point state of the t-J model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at finite doping so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic residual couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at (\ensuremath{\pi}/a,\ensuremath{\pi}/a) with a doping-dependent width (\ensuremath{\propto} \ensuremath{\surd}\ensuremath{\delta} , \ensuremath{\delta} is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exists a characteristic temperature scale below thich a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a finite energy regime. In the transport, a strong-range phase intereference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-T resistivity and a T2{\mathit{T}}^{2}T2 Hall angle. We discuss the striking similarities of these theoretical features with those found in the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates and give a consistent picture for the latter. Electronic properties like Fermi surface and superconducting pairing in this framework are also discussed.