  To elucidate a quantum phase transition (QPT) in
Bi_2Sr_{2-x}La_xCuO_{6+\delta}, we measure charge and heat transport properties
at very low temperatures and examine the following characteristics for a wide
range of doping: normal-state resistivity anisotropy under 58 T, temperature
dependence of the in-plane thermal conductivity K_{ab}, and the magnetic-field
dependence of K_{ab}. It turns out that all of them show signatures of a QPT at
the 1/8 hole doping. Together with the recent normal-state Hall measurements
under 58 T that signified the existence of a QPT at optimum doping, the present
results indicate that there are two QPTs in the superconducting doping regime
of this material.
