Many phases of matter are characterized by order of some electronic degree of freedom such as spin (as in the case of spin density waves - SDW), or charge (as in the case of charge density waves - CDW). Other phases are characterized by more complicated order parameters that are directly related to many-body effects (as in the casea of superconductivity). It is possible to tune between phases with order and without order by tunning some parameter such as the temperature of the system. These finite temperature phase transititons have been well studied in the context of classical critical phenomena. Much less is known by phase transitions that occur at zero temperature in which quantum fluctuations play an important role.These quantum phase transitions (QPT) are responsible for very unusual behavior that cannot be described within traditional theoretical frameworks. QPT transitions can be tuned by the application of pressure, magnetic field, or even chemical modification, that unavoidably introduces disorder in the material. Disorder can strongly affect QPT because quantum fluctuations are very sensitive to geometrical constraints. Cold atom systems, high temperature superconductors, transition metal dichalcogenides, and heavy fermion materials are example of systems where QPT are believed to play an important role.


Example of a Quantum Phase Transition: T is temperature and Fm is a tunning parameter.