Quantum Critical Scaling in a Moderately Doped Antiferromagnet

TL;DR

This paper provides evidence of quantum critical behavior in a doped antiferromagnet using high temperature expansions, showing universal scaling and agreement with experimental nuclear relaxation rates in cuprates.

Contribution

It demonstrates quantum critical scaling in the t-J model at intermediate temperatures, linking theoretical predictions with experimental observations in cuprate materials.

Findings

Quantum critical behavior observed at intermediate temperatures.

Dynamical susceptibility matches universal scaling functions.

Results agree with experimental nuclear relaxation rates in cuprates.

Abstract

Using high temperature expansions for the equal time correlator $S(q)$ and static susceptibility $\chi(q)$ for the t-J model, we present evidence for quantum critical (QC), $z\!=\!1$, behavior at intermediate temperatures 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, $1/T_{\rm 2G}$, in La$_2$CuO$_4$, and provide qualitative understanding of both $1/T_1$ and $1/T_{\rm 2G}$ nuclear relaxation rates in doped cuprates.