The melting of ice is, like most phase transitions, caused by the increase in random thermal motion of the molecules which occurs as the temperature is raised. The ordered arrangement of atoms that exists in the solid cannot be sustained beyond a certain temperature and the crystal melts. Yet research into condensed matter over the past decade has revealed a new kind of phase transition that is driven, not by thermal motion, but by the quantum fluctuations associated with Heisenberg’s uncertainty principle. These quantum fluctuations are called ‘zero-point motion’. According to the uncertainty principle, the more certain a particle’s position, the more uncertain is its velocity. Thus, even when random, thermal motion ceases at the absolute zero temperature, atoms and molecules cannot be at rest because this would simultaneously fix their position and velocity. Instead they adopt a state of constant agitation. Like thermal motion, if zero-point motion becomes too wild, it can melt order, but in this case the melting takes place at absolute zero. Such a quantum phase transition[3] takes place in solid helium, which is so fragile that it requires a pressure to stabilize its crystal lattice even at absolute zero. When the pressure is released, zero-point motions melt the crystal.
The best studied examples of quantum phase transitions involve magnetism in metals. Electrons have a magnetic direction or spin, which when aligned in a regular fashion makes a material magnetic. Iron magnetizes when all the spins inside align in parallel, but in other materials the spins form a staggered, alternating, or antiferromagnetic, arrangement (Fig. 1). These more fragile types of order are more susceptible to melting by zero-point fluctuations. Almost three decades ago theoretical physicist John Hertz, now at Nordita, made the first study of how quantum mechanics would affect phase transitions[4]. Hertz was fascinated by the question of how critical phenomena might be altered by quantum mechanics. Applying quantum mechanics to phase transitions turns out to be very like Einstein’s relativistic unification of space-time. In Hertz’s theory, quantum mechanics appears by including a time dimension to the droplets of nascent order. Normally this produces no additional effect, but Hertz reasoned that if a phase transition took place at absolute zero, then the4 droplets of order that foreshadow the transition would become quantum-mechanical rather than classical. At a zero-temperature phase transition, he reasoned, these quantum droplets would grow to dominate the entire material, changing its properties in measurable ways—and most affected would be the electrons (Fig. 2). Such ‘quantum critical matter’ offers the real prospect of new classes of universal electronic behaviour developing independently of the detailed material behaviour, once the material is driven close to a quantum critical point.
