Quantum critical scaling in a moderately doped antiferromagnet

Using high temperature expansions for the equal time correlator S(q) and static susceptibility χ(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/${\mathit{T}}_{2\mathrm{G}}$, in ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$, and provide qualitative understanding of both 1/${\mathit{T}}_1$ and 1/${\mathit{T}}_{2\mathrm{G}}$ nuclear relaxation rates in doped cuprates.