Phases of SU(2) gauge theory with multiple adjoint Higgs fields in 2+1 dimensions

TL;DR

This paper analyzes a SU(2) gauge theory with multiple adjoint Higgs fields in 2+1 dimensions, revealing phases that correspond to different states of cuprate superconductors, including confining and topologically ordered Higgs phases.

Contribution

It provides a strong-coupling analysis of the gauge theory, identifying confining and Higgs phases with distinct symmetry-breaking patterns and topological properties, relevant to cuprate physics.

Findings

Identified a confining phase with preserved O(N_h) symmetry.

Discovered Higgs phases with different symmetry-breaking patterns.

Found a topologically trivial Higgs phase and a Z2 topological order phase.

Abstract

A recent work (arXiv:1811.04930) proposed a SU(2) gauge theory for optimal doping criticality in the cuprate superconductors. The theory contains $N_h$ Higgs fields transforming under the adjoint representation of SU(2), with $N_h=1$ for the electron-doped cuprates, and $N_h=4$ for the hole-doped cuprates. We investigate the strong-coupling dynamics of this gauge theory, while ignoring the coupling to fermionic excitations. We integrate out the SU(2) gauge field in a strong-coupling expansion, and obtain a lattice action for the Higgs fields alone. We study such a lattice action, with O($N_h$) global symmetry, in an analytic large $N_h$ expansion and by Monte Carlo simulations for $N_h=4$ and find consistent results. We find a confining phase with O($N_h$) symmetry preserved (this describes the Fermi liquid phase in the cuprates), and Higgs phases (describing the pseudogap phase of the cuprates) with different patterns of the broken global O($N_h$) symmetry. One of the Higgs phases is topologically trivial, implying the absence of any excitations with residual gauge charges. The other Higgs phase has $\mathbb{Z}_2$ topological order, with `vison' excitations carrying a $\mathbb{Z}_2$ gauge charge. We find consistent regimes of stability for the topological Higgs phase in both our numerical and analytical analyses.