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 copperperovskite 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. 