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

## Abstract

Here, 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.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

- OSTI Identifier:
- 1564362

- Alternate Identifier(s):
- OSTI ID: 1469019

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Published Article

- Journal Name:
- Science Bulletin

- Additional Journal Information:
- Journal Name: Science Bulletin Journal Volume: 63 Journal Issue: 12; Journal ID: ISSN 2095-9273

- Publisher:
- Elsevier

- Country of Publication:
- China

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; Topological Luttinger liquids; Symmetry protected topological phase; Phase transition; Superconductivity; Density-matrix renormalization group

### Citation Formats

```
Jiang, Hong-Chen, Li, Zi-Xiang, Seidel, Alexander, and Lee, Dung-Hai. Symmetry protected topological Luttinger liquids and the phase transition between them. China: N. p., 2018.
Web. doi:10.1016/j.scib.2018.05.010.
```

```
Jiang, Hong-Chen, Li, Zi-Xiang, Seidel, Alexander, & Lee, Dung-Hai. Symmetry protected topological Luttinger liquids and the phase transition between them. China. https://doi.org/10.1016/j.scib.2018.05.010
```

```
Jiang, Hong-Chen, Li, Zi-Xiang, Seidel, Alexander, and Lee, Dung-Hai. Fri .
"Symmetry protected topological Luttinger liquids and the phase transition between them". China. https://doi.org/10.1016/j.scib.2018.05.010.
```

```
@article{osti_1564362,
```

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

author = {Jiang, Hong-Chen and Li, Zi-Xiang and Seidel, Alexander and Lee, Dung-Hai},

abstractNote = {Here, 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.},

doi = {10.1016/j.scib.2018.05.010},

journal = {Science Bulletin},

number = 12,

volume = 63,

place = {China},

year = {2018},

month = {6}

}

https://doi.org/10.1016/j.scib.2018.05.010

*Citation information provided by*

Web of Science

Web of Science

Works referencing / citing this record:

##
Asymptotic Correlations in Gapped and Critical Topological Phases of 1D Quantum Systems

journal, April 2019

- Jones, N. G.; Verresen, R.
- Journal of Statistical Physics, Vol. 175, Issue 6

##
Emergent mode and bound states in single-component one-dimensional lattice fermionic systems

journal, November 2019

- He, Yuchi; Tian, Binbin; Pekker, David
- Physical Review B, Vol. 100, Issue 20

##
Full commuting projector Hamiltonians of interacting symmetry-protected topological phases of fermions

journal, October 2018

- Tantivasadakarn, Nathanan; Vishwanath, Ashvin
- Physical Review B, Vol. 98, Issue 16

##
Nontopological Majorana Zero Modes in Inhomogeneous Spin Ladders

journal, January 2019

- Robinson, Neil J.; Altland, Alexander; Egger, Reinhold
- Physical Review Letters, Vol. 122, Issue 2