# Symmetry protected topological Luttinger liquids and the phase transition between them

## 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 $$d_{xy}$$ in the non-trivial phase and triplet $$S_z=0$$ 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.

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1437660

- DOE Contract Number:
- AC02-76SF00515

- Resource Type:
- Program Document

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

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```*Symmetry protected topological Luttinger liquids and the phase transition between them*. United States: N. p., 2018.
Web.

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```*Symmetry protected topological Luttinger liquids and the phase transition between them*. United States.

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"Symmetry protected topological Luttinger liquids and the phase transition between them". United States. https://www.osti.gov/servlets/purl/1437660.
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@article{osti_1437660,
```

title = {Symmetry protected topological Luttinger liquids and the phase transition between them},

author = {None},

abstractNote = {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. 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.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2018},

month = {1}

}