Spin-Charge Separation in the $t-J$ Model: Magnetic and Transport Anomalies

TL;DR

This paper presents a spin-charge separation scheme in the $t-J$ model, revealing magnetic and transport anomalies at finite doping that resemble phenomena observed in high-$T_c$ cuprates, including pseudogap behavior and non-Fermi liquid features.

Contribution

It introduces a novel saddle-point state demonstrating spin-charge deconfinement in 2D at finite doping, explaining anomalies in magnetic and transport properties.

Findings

Gapped gauge field at finite doping leads to spin-charge deconfinement in 2D.

Doping-dependent antiferromagnetic fluctuations with Gaussian peaks.

Linear-$T$ resistivity and $T^2$ Hall-angle phenomena in transport.

Abstract

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 {\em 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 {\em 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 ($\pi/a$, $ \pi/a$) with a doping-dependent width ($\propto \sqrt{\delta}$, $\delta$ is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exits a characteristic temperature scale below which a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a {\em finite} energy regime. In transport, a strong short-range phase interference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-$T$ resistivity and $T^2$ Hall-angle. We discuss the striking similarities of these theoretical features with those found in the high-$T_c$ cuprates and give a