# Gapless Symmetry-Protected Topological Order

## Abstract

We introduce exactly solvable gapless quantum systems in d dimensions that support symmetry-protected topological (SPT) edge modes. Our construction leads to long-range entangled, critical points or phases that can be interpreted as critical condensates of domain walls “decorated” with dimension ( d - 1 ) SPT systems. Using a combination of field theory and exact lattice results, we argue that such gapless SPT systems have symmetry-protected topological edge modes that can be either gapless or symmetry broken, leading to unusual surface critical properties. Despite the absence of a bulk gap, these edge modes are robust against arbitrary symmetry-preserving local perturbations near the edges. In two dimensions, we construct wave functions that can also be interpreted as unusual quantum critical points with diffusive scaling in the bulk but ballistic edge dynamics.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

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

- OSTI Identifier:
- 1412946

- Alternate Identifier(s):
- OSTI ID: 1485068

- Grant/Contract Number:
- AC02-05CH11231

- Resource Type:
- Published Article

- Journal Name:
- Physical Review. X

- Additional Journal Information:
- Journal Name: Physical Review. X Journal Volume: 7 Journal Issue: 4; Journal ID: ISSN 2160-3308

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Scaffidi, Thomas, Parker, Daniel E., and Vasseur, Romain. Gapless Symmetry-Protected Topological Order. United States: N. p., 2017.
Web. doi:10.1103/PhysRevX.7.041048.
```

```
Scaffidi, Thomas, Parker, Daniel E., & Vasseur, Romain. Gapless Symmetry-Protected Topological Order. United States. doi:10.1103/PhysRevX.7.041048.
```

```
Scaffidi, Thomas, Parker, Daniel E., and Vasseur, Romain. Wed .
"Gapless Symmetry-Protected Topological Order". United States. doi:10.1103/PhysRevX.7.041048.
```

```
@article{osti_1412946,
```

title = {Gapless Symmetry-Protected Topological Order},

author = {Scaffidi, Thomas and Parker, Daniel E. and Vasseur, Romain},

abstractNote = {We introduce exactly solvable gapless quantum systems in d dimensions that support symmetry-protected topological (SPT) edge modes. Our construction leads to long-range entangled, critical points or phases that can be interpreted as critical condensates of domain walls “decorated” with dimension ( d - 1 ) SPT systems. Using a combination of field theory and exact lattice results, we argue that such gapless SPT systems have symmetry-protected topological edge modes that can be either gapless or symmetry broken, leading to unusual surface critical properties. Despite the absence of a bulk gap, these edge modes are robust against arbitrary symmetry-preserving local perturbations near the edges. In two dimensions, we construct wave functions that can also be interpreted as unusual quantum critical points with diffusive scaling in the bulk but ballistic edge dynamics.},

doi = {10.1103/PhysRevX.7.041048},

journal = {Physical Review. X},

number = 4,

volume = 7,

place = {United States},

year = {2017},

month = {11}

}

DOI: 10.1103/PhysRevX.7.041048

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

*d*example. (a) Trivial: Paramagnetic spins on a triangular lattice with fluctuating domain walls. (b) SPT: Decorating the domain walls, giving a SPTwith a

*c*= 1 edge mode. (c) Gapless trivial: Tuning the domain walls to criticality by restricting themmore »

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Works referencing / citing this record:

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Topologically Protected Long Edge Coherence Times in Symmetry-Broken Phases

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Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*