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

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.

arXiv comment23 pages, 4 figures

References in corpus (10)

• "Deconfined" quantum critical points
• Spectral functions of the Higgs mode near two-dimensional quantum critical points
• Topological order in the pseudogap metal
• Pseudogap and Fermi surface topology in the two-dimensional Hubbard model
• Exact relation of lattice and continuum parameters in three-dimensional SU(2)+Higgs theories
• Gauge theory for the cuprates near optimal doping
• Fermi surface reconstruction in electron-doped cuprates without antiferromagnetic long-range order
• Phase diagram, symmetry breaking, and critical behavior of three-dimensional lattice multiflavor scalar chromodynamics
• The monopole mass in the three-dimensional Georgi-Glashow model
• Criticality of O(N) symmetric models in the presence of discrete gauge symmetries

Cited by in corpus (13)

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• Three-dimensional lattice SU($N_c$) gauge theories with multiflavor scalar fields in the adjoint representation
• Phase diagram and Higgs phases of 3D lattice SU(Nc) gauge theories with multiparameter scalar potentials
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Two-dimensional lattice SU($N_c$) gauge theories with multiflavor adjoint scalar fields
• Critical relaxational dynamics at the continuous transitions of three-dimensional spin models with ${\mathbb{Z}}_2$ gauge symmetry
• Non-compact lattice Higgs model with Abelian discrete gauge groups: phase diagram and gauge symmetry enlargement
• Charged critical behavior and nonperturbative continuum limit of three-dimensional lattice SU($N_c$) gauge Higgs models
• Bilocal quantum criticality
• Modified Abelian and SU(2) Wilson theories on a lattice from a non-compact regularization
• Color-flavor reflection in the continuum limit of two-dimensional lattice gauge theories with scalar fields