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Updated: Aug 13, 2025

Phase Diagram Characterization Using Magnetic Beads as Liquid Carriers
Published on: September 4, 2015
Symmetry protected topological Luttinger liquids and the phase transition between them
Hong-Chen Jiang1, Zi-Xiang Li2, Alexander Seidel3
1Stanford Institute for Materials and Energy Science, SLAC and Stanford University, Menlo Park, CA 94025, USA.
Abstract:
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 dxy in the non-trivial phase and triplet Sz=0 in the trivial phase. The topologically non-trivial Luttinger liquid exhibits gapless spin excitations in the presence of a boundary, and it has no non-interacting or mean-field theory analog even when the fluctuating phase in the charge sector is pinned. As a function of the strength of spin anisotropy there is a topological phase transition upon which the spin gap closes. We speculate these Luttinger liquids are relevant to the superconductivity in metalized integer spin ladders or chains.
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