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

摘要

A recent work [S. Sachdev et al., Phys. Rev. B 99, 054516 (2019)] 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 Z_2 topological order, with "vison" excitations carrying a Z_2 gauge charge. We find consistent regimes of stability for the topological Higgs phase in both our numerical and analytical analyses.