Symmetry protected topological Luttinger liquids and the phase transition between them

Understand

We show that a doped spin-1/2 ladder with antiferromagnetic intra-chain and ferromagnetic inter-chain coupling is a symmetry protected topologically non-trivial Luttinger liquid.

• Turning on a large easy-plane spin anisotropy drives the system to a topologically-trivial Luttinger liquid.
• Both phases have full spin gaps and exhibit power-law superconducting pair correlation.
• The Cooper pair symmetry is singlet $d_{xy}$ in the non-trivial phase and triplet $S_z=0$ in the trivial phase.