ABSTRACT
In the previous chapter, we discussed both the insulator-superconductor and the insulator-metal transitions. As such transitions are disorder- or magnetic field-tuned, thermal fluctuations play no role. Phase transitions of the insulator-superconductor or insulator-metal type are called quantum phase transitions. Such phase transitions are not controlled by changing the temperature, as in the melting of ice or the λ-point of liquid helium, but rather by changing some system parameter, such as the number of defects or the concentration of charge carriers. In all such instances, the tuning parameter transforms the system between quantum mechanical states that either look different topologically (as in the transition between localized or extended electronic states) or have distinctly different magnetic properties. As quantum mechanics underlies such phase transitions, all quantum phase transitions obtain at the absolute zero of temperature and thus are governed by a T = 0 quantum critical point. Although initially surprising, this state of affairs is expected, because quantum mechanics is explicitly a zero-temperature theory of matter. Of course, this is no surprise to chemists, who have known for quite some time that numerous materials can exhibit vastly distinct properties simply by changing the chemical composition and, most importantly, that such transformations persist down to zero temperature. Common examples include turning insulators, such as the layered cuprates, into superconductors simply by chemical doping, or semiconductors into metals, once again by doping, or ferromagnets, such as Li (Ho, Tb)x Y 1- xF 4, into a spin glass [AR1998] by altering x. Certainly, the technological relevance of doped semiconductors, the backbone of the electronics industry, is well established.
