Exotic phases and quantum criticality in gapless correlated electron systems

Abstract

In this thesis, I theoretically studied exotic phases of matter than arise due to strong interactions between electrons in three different scenarios. Firstly, at a stripe melting phase transition, which may be relevant for the high temperature superconductors, where we propose a specific type of transition which produces critical exponents agreeing with neutron scattering experiments on LSCO. Secondly, for a Pomeranchuk transition where an electronic nematic order parameter develops we present a controlled expansion within which the physics of such a transition, and of the related problem of fermions coupled to a gauge field, can be addressed. Thirdly, in a quantum spin liquid phase that is likely to be realized in certain organic Mott insulators. Here we show how such a phase can be accessed from a low energy description of a metal, without resorting to slave-particle constructions. Methodologically, the work in this thesis relies on field theoretical methods such as the renormalization group, the large-N and related expansions, dualities, bosonization and slave-particle constructions.