Dynamic spin susceptibility in the t-J model

TL;DR

This paper develops a relaxation-function theory for the dynamic spin susceptibility in the t-J model, accurately capturing spin dynamics across doping levels and temperatures, and aligning well with experimental and numerical data.

Contribution

It introduces a sum-rule-conserving GMFA and mode-coupling approximation to analyze spin susceptibility and dynamics in the t-J model, extending understanding beyond previous methods.

Findings

Good agreement with exact diagonalization data

Spin-wave behavior at low doping, relaxation dynamics at high doping

Local spin susceptibility and (/T) scaling match experiments

Abstract

A relaxation-function theory for the dynamic spin susceptibility in the $t$--$J$ model is presented. By a sum-rule-conserving generalized mean-field approximation (GMFA), the two-spin correlation functions of arbitrary range, the staggered magnetization, the uniform static susceptibility, and the antiferromagnetic correlation length are calculated in a wide region of hole doping and temperaturs. A good agreement with available exact diagonalization (ED) data is found. The correlation length is in reasonable agreement with neutron-scattering experiments on La_{2-\delta}Sr_\delta)CuO_4. Going beyond the GMFA, the self-energy is calculated in the mode-coupling approximation. The spin dynamics at arbitrary frequencies and wave vectors is studied for various temperatures and hole doping. At low doping a spin-wave-type behavior is found as in the Heisenberg model, while at higher doping a strong damping caused by hole hopping occurs, and a relaxation-type spin dynamics is observed in agreement with the ED results. The local spin susceptibility and its (\omega/T) scaling behavior are calculated in a reasonable agreement with experimental and ED data.