Computational studies of quantum phase transitions

Anders Sandvik

A continuous ground state phase transition occurring in a quantum-mechanical many-particle system as a function of some system parameter is referred to as a quantum phase transition. At the quantum-critical point separating two different types of ground states, the quantum fluctuations play a role analogous to thermal fluctuations in a phase transition occurring at nonzero temperature. An important aspect of these transitions is that the critical fluctuations and the associated scaling behavior of the quantum-critical point influences the system not only in the close vicinity of the ground-state critical point itself, but also in a wide finite-temperature region surrounding it. While many quantum phase transitions can be understood in terms of a mapping of the quantum mechanical problem onto a classical statistical-mechanics problem with an additional dimension (corresponding to time), recent attention has been focused on exotic transitions which fall outside the classical framework and may be important in strongly-correlated electronic systems such as the high-Tc cuprate superconductors. Prof. Sandvik’s group uses quantum Monte Carlo techniques to explore such transitions in model systems, primarily quantum spin systems. The purpose of this research is to find and characterize various quantum phase transitions in an un-biased (non-approximate) way, in order to provide benchmarks and guidance to developing theories. The influence of disorder (randomness) on the nature of quantum phase transitions is also studied.