Exotic phases and quantum phase transitions: model systems and experiments

The band theory of electrons predicts that any crystal with an odd number of electrons per unit cell must be a metal. However, strong electron-electron interactions can invalidate this conclusion, and such crystals can also be insulators, known as Mott insulators. I will use this term here more broadly: often the Mott insulator has a secondary instability to spin or charge ordering which increases the size of the unit cell, so that the ultimate ground state of the insulator does have an even number of electrons per unit cell (many examples of such instabilities will be discussed below). I will continue to refer to such insulators as Mott insulators because electron-electron interactions are crucial to understanding their broken symmetries and excitation spectrum. In contrast, describing the ordering by using the instabilities of a metallic state with an odd number of electrons per unit cell leads to a rather poor understanding of the insulator and of the energy scales characterizing its excitations. A canonical model used to study Mott insulators is the single-band Hubbard model