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arXiv · 1912.06108

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

Harley D. Scammell·Kartik Patekar·Mathias S. Scheurer·Subir Sachdev
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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.

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Harley D. Scammell, Kartik Patekar, Mathias S. Scheurer, Subir Sachdev. 2019-12-12. Phases of SU(2) gauge theory with multiple adjoint Higgs fields in 2+1 dimensions. https://doi.org/10.1103/physrevb.101.205124

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