ABSTRACT
Anatoli Polkovnikov Department of Physics, Boston University, 590 Commonwealth Ave., Boston, MA 02215, U.S.A.
Vladimir Gritsev Physics Department, University of Fribourg, Chemin du Musee 3, 1700 Fribourg, Switzerland
Continuous quantum phase transitions (QPTs) have been a subject of intense theoretical research in recent decades (see, e.g., Refs. [1-3] for overview). Unlike usual phase transitions driven by temperature, QPTs are driven entirely by quantum fluctuations. They are believed to occur in many situations as described later in this book. Quite recently a second order QPT was observed in a cold atom system of interacting bosons in an optical lattice. There a system of interacting bosons was driven in real time from the superfluid to the insulating phase [4], confirming an earlier theoretical prediction [5]. Up till now, Ref. [4] has provided probably the cleanest experimental confirmation of a QPT. The unifying property of all continuous (second order) phase transitions is the emergent universality and scale invariance of the long-distance low energy properties of the system near the quantum critical point (QCP) [1]. This universality implies that low-energy properties of the system can be described by very few parameters, like the correlation length or the gap, which typically have power-law scaling with the tuning parameter characterized by critical exponents. These exponents are not sensitive to the microscopic details of the Hamiltonian describing the system, but rather depend only on the universality class to which a given phase transition belongs [1].
