Universality of Charge and Spin Response in Doped Antiferromagnets

TL;DR

This paper reviews numerical results on the universal charge and spin response functions in doped antiferromagnets, highlighting their temperature and doping independence and connection to experimental observations in cuprates.

Contribution

It introduces a novel numerical method for small correlated systems and demonstrates universal features in charge and spin responses at finite temperatures.

Findings

Charge and spin responses are universal at intermediate doping.

The current correlation function is nearly temperature- and frequency-independent below J.

Results connect to experimental data on cuprates and suggest large entropy effects.

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 $\sigma(\omega)$ and spin susceptibility $\chi(\vec q,\omega)$, 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 $\sigma(\omega)$ we find that the current correlation function $C(\omega)$ is nearly $T$- and moreover $\omega$-independent in the regime $T <J$, leading to the $\sigma(\omega)$ behavior, very close to the marginal Fermi liquid concept and experiments. These properties are interpreted in connection with the large entropy, related to the large degeneracy of the low-lying states and quantum frustration in the doped antiferromagnets. On the other hand, results for the uniform susceptibility $\chi_0(T)$, as well as for the $\sigma(\omega)$, reveal qualitative changes on entering the underdoped regime.