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Scientific Background

Scientific advances in the 20^th Century

The Frontier Science of Emergent Materials

The idea of criticality

One of the new ideas to emerge in condensed matter physics at the beginning of this century, is that of quantum phase transitions. Classical phase transitions, such as the crystallization of water vapor into snow flakes on cold day or the magnetization of a metal pin, are associated with changes in the jiggling random thermal motions inside the material. The last decade has seen the discovery of a new kind of phase transition, where the changes in order result from not from thermal fluctuations, but quantum mechanical fluctuations.
According to the pioneering work by Lev Landau in the 1940s, the development of new properties inside a material occurs the emergence of an "order parameter": a quality which describes the state of developing order at each point in the material, such as the local magnetic polarization of a ferromagnet, or the mysterious "psi" (y) field that describes the collective wavefunction of an electron condensate inside a superconductor, or an atom collective within a Bose Einstein Condensate. Materials which undergo a phase transition often develop a “broken symmetry”.	Lev Landau
Classical phase transitions occur at a finite temperature, A material that is tuned close to a classical phase transition senses the imminent change of state as the order parameter develops thermal fluctuations over larger and larger regions of the sample: such a state is known as a "critical state". The understanding of such classical criticality is one of the triumphs of twentieth century condensed matter physics. Moreover, in the process of understanding the critical state of matter physicists developed of a new conceptual framework called the "renormalization group" , which links the behavior of matter at different length scales. The renormalization group concept and mathematics has had wide impact throughout both condensed matter and particle physics.
	The development of an order parameter gives rise to new properties. In the case of superconductivity, the development of a “pair condensate” associated with an order parameter "psi" (y), leads to the ability to expel magnetic fields. This property makes it possible to magnetically levitate superconductors, such as this chunk of high temperature superconductor, shown here.
“Quantum Criticality” involves a completely new class of transformation in material properties. A quantum critical point (QCP) occurs when the phase transition temperature of a material is suppressed to absolute zero. The concept of quantum criticality was introduced to physics in 1970s by John Hertz, but was thought to be of purely academic interest. Today the phenomenon of quantum phase transitions has emerged as a major challenge to our understanding of condensed matter. Recent experiments have revealed the ability of quantum phase transitions to qualitatively transform the electronic properties of a material at finite temperatures. For example, high temperature superconductivity is thought to be born from a new metallic state that develops at a certain critical doping in copper-perovskite materials. A material that is tuned to a quantum critical point enters a weird state of "quantum criticality". Every site in a material at quantum criticality develops a quantum superposition of order and disorder in just the same way that Schrodinger's hypothetical cat is in a quantum superposition of "dead" and "alive". For this reason, quantum fluctuations of the underlying order parameter develop over infinite regions of both space and time inside the crystal. It is these mysterious fluctuations that physicists do not yet understand, but which are thought to be responsible for the profound transformations in material property that have been found to develop near a quantum phase transition.
	A material that is tuned to a quantum critical point (QCP) enters a weird state of "quantum criticality". Every site in a material at quantum criticality develops a quantum superposition of order and disorder in just the same way that Schrodinger's hypothetical cat is in a quantum superposition of "dead" and "alive". For this reason, quantum fluctuations of the underlying order parameter develop over infinite regions of both space and time inside the crystal. These quantum fluctuations are responsible for the profound transformations in electronic properties, that have been found to develop near a quantum phase transition.
The development of a unified understanding of thermal phase transitions and “classical criticality” was a triumph of the 20th century. We are still far from a complete understanding of quantum phase transitions, but already, many suspect that the ultimate solution to this problem may be needed to understand and ultimately control phenomena such as high temperature superconductivity will depend on the development of a new theory of quantum phase transitions.
The meeting at Columbia from the 20^th-23^rd March will bring together experts from Europe, America and Japan to discuss, in an informal setting, the problem of quantum criticality, and in a more general setting, the physics of emergent materials. The meeting will endeavor to bring some of the excitement of this field to the press and the public, and the event will be filmed with the view to a future documentary on the frontier physics of emergent collective matter.