Strongly coupled quantum criticality with a Fermi surface in two dimensions: fractionalization of spin and charge collective modes

TL;DR

This paper investigates quantum phase transitions in two-dimensional metallic systems with a Fermi surface, focusing on topological order parameters and fractionalization phenomena relevant to cuprate superconductors.

Contribution

It introduces models with topological order parameters linked to spin density wave dislocations, analyzing their critical behavior and coupling effects via renormalization group methods.

Findings

Identification of runaway RG flows indicating non-perturbative regimes

Proposal of phenomenological scaling forms for observable properties

Connection of critical behavior to phenomena in cuprate superconductors

Abstract

We describe two dimensional models with a metallic Fermi surface which display quantum phase transitions controlled by strongly interacting critical field theories below their upper critical dimension. The primary examples involve transitions with a topological order parameter associated with dislocations in collinear spin density wave ("stripe") correlations: the gapping of the order parameter fluctuations leads to a fractionalization of spin and charge collective modes, and this transition has been proposed as a candidate for the cuprates near optimal doping. The coupling between the order parameter and long-wavelength volume and shape deformations of the Fermi surface is analyzed by the renormalization group, and a runaway flow to a non-perturbative regime is found in most cases. A phenomenological scaling analysis of simple observable properties of possible second order quantum critical points is presented, with results quite similar to those near quantum spin glass transitions and to phenomenological forms proposed by Schroeder et al. (cond-mat/0011002).