Sharp signature of DDW quantum critical point in the Hall coefficient of the cuprates

We study the behavior of the Hall coefficient, $R_H$, in a system exhibiting $d_{x^2-y^2}$ density-wave (DDW) order in a regime in which the carrier concentration, $x$, is tuned to approach a quantum critical point at which the order is destroyed. At the mean-field level, we find that $n_{\mathrm{H}\mathrm{a}\mathrm{l}\mathrm{l}}=1\mathrm{/}{R}_H$ evinces a sharp signature of the transition. There is a kink in $n_{\mathrm{H}\mathrm{a}\mathrm{l}\mathrm{l}}$ at the critical value of the carrier concentration, $x_c$; as the critical point is approached from the ordered side, the slope of $n_{\mathrm{H}\mathrm{a}\mathrm{l}\mathrm{l}}$ diverges. Hall transport experiments in the cuprates, at high magnetic fields sufficient to destroy superconductivity, should reveal this effect.