Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems

TL;DR

This paper introduces a Z_2 gauge theory framework to describe electron fractionalization in strongly correlated systems, revealing exotic phases like fractionalized insulators and superconductors, with implications for high-temperature superconductivity.

Contribution

It develops a new Z_2 gauge theory approach that captures fractionalization and exotic phases in strongly correlated electron systems, bridging insulators and superconductors.

Findings

Identification of a fractionalized insulator called the nodal liquid.

Demonstration of a Z_2 gauge theory interpolating between antiferromagnetic insulator and d-wave superconductor.

Description of vortex dynamics and fractionalization mechanisms in 2D systems.

Abstract

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 Z_2 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 Z_2 gauge field. Fractionalization is obtained if they are uncondensed. Within the insulating phases, the dynamics of these Z_2 vortices in two dimensions (2d) is described, after a duality transformation, by an Ising model in a transverse field - the Ising spins representing the Z_2 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 Z_2 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.