Spin-gapped phases in the frustrated Hubbard chain with transverse spin anisotropy

At weak coupling, we investigate the frustrated Hubbard chain including nearest-neighbor and next-nearest-neighbor antiferromagnetic exchange with easy-plane anisotropy $J_1^{xy}$ and $J_2^{xy}$. At half filling, we obtain three different phases in the $J_1^{xy}$–${J_2}^{xy}$ plane: a transverse spin density wave phase, a bond order wave phase and a Luther–Emery metallic phase characterized by the coexistence of singlet superconductivity and charge density wave correlations. The frustrating exchange $J_2^{xy}$ accounts for the spin-gapped phases.