Anomalous critical behavior near the quantum critical point of a hole-doped La$_2$CuO$_4$

In zero temperature quantum critical phenomena, classical thermal fluctuations are replaced by zero-point quantum critical phenomena and quantum mechanical generalization of the Landau-Ginzburg- Wilson paradigm has been a central topic in condensed matter physics. In Sr or Ba-doped La$_2$CuO$_4$, which is a member of high-Tc superconducting cuprates, the energy spectra of spin fluctuations in the neighborhood of the ($\pi,\pi$) antiferromagnetic Bragg point have been shown to follow the $E/T$ scaling. In the neutron scattering study on spin dynamics in La$_2$Cu$_{1-x}$Li$_{x}$O$_4$, we find that the critical exponent $a$ in the $E/T$ scaling changes from an expected $a$ $\approx$ 1 to an anomalous $a$ $\approx$ 0.65 and the scaling function becomes anomalous when the doping is reduced towards the antiferromagnetic quantum critical point, which has not been expected in the current theories.[1] Our results suggests extra physics which is beyond mapping the 2-dimensional quantum spin system to a 3 dimensional one in classical Landau-Ginzburg-Wilson theory. [1] Y. Chen {\it et al.}, cond-matt/0408547