Quantum Criticality: competing ground states in low dimensions

Abstract

Small changes in an external parameter can often lead to dramatic qualitative changes in the lowest energy quantum mechanical ground state of a correlated electron system. In anisotropic crystals, such as the high temperature superconductors where electron motion occurs primarily on a two-dimensional square lattice, the quantum critical point between two such lowest energy states has non-trivial emergent excitations which control the physics over a significant portion of the phase diagram. Non-zero temperature dynamic properties near quantum critical points are described using simple theoretical models. Possible quantum phases and transitions of the two-dimensional electron gas on a square lattice are discussed, including phases with spin-charge separation and their experimental signatures.

(v1) Non-technical review article published in April 2000; new footnotes have been added to the cond-mat version; 19 pages and 7 color figures. (v2) Expanded the new footnotes. (v3) Added reference to paper by McQueeney et al reporting experimental evidence for the theoretically predicted spin-Peierls order in the high temperature superconductors; thanks to S. Kivelson for pointing out this experiment