1999/10/21 by T. Senthil, Matthew P. A. Fisher · 2 citations
Physics and Astronomy · #cond-mat.str-el #cond-mat.supr-con
paper · pdf · doi:10.1103/physrevb.62.7850
36 pages, 9 figures; one reference added
arxiv created 1999/10/21 · arxiv updated 2009/11/30
We develop a new theoretical framework for describing and analyzing exotic phases of strongly correlated electrons which support excitations with fractional quantum numbers. Starting with a class of microscopic models believed to capture much of the essential physics of the cuprate superconductors, we derive a new gauge theory - based upon a \it discrete Ising or Z2 symmetry - which interpolates naturally between an antiferromagnetic Mott insulator and a conventional d-wave superconductor. We explore the intervening regime, and demonstrate the possible existence of an exotic fractionalized insulator - the nodal liquid - as well as various more conventional insulating phases exhibiting broken lattice symmetries. A crucial role is played by vortex configurations in the Z2 gauge field. Fractionalization is obtained if they are uncondensed. Within the insulating phases, the dynamics of these Z2 vortices in two dimensions (2d) is described, after a duality transformation, by an Ising model in a transverse field - the Ising spins representing the Z2 vortices. The presence of an unusual Berry's phase term in the gauge theory, leads to a doping-dependent "frustration" in the dual Ising model, being fully frustrated at half-filling. The Z2 gauge theory is readily generalized to a variety of different situations - in particular, it can also describe 3d insulators with fractional quantum numbers. We point out that the mechanism of fractionalization for d>1 is distinct from the well-known 1d spin-charge separation. Other interesting results include a description of an exotic fractionalized superconductor in two or higher dimensions.