# A holographic theory for the phase transitions between fermionic symmetry-protected topological states

## Abstract

In an earlier work we developed a holographic theory for the phase transition between bosonic symmetry-protected topological (SPT) states. This paper is a continuation of it. Here we present the holographic theory for fermionic SPT phase transitions. We show that in any dimension d, the critical states of fermionic SPT phase transitions has an emergent Z$$_2^T$$ symmetry and can be realized on the boundary of a d+1-dimensional bulk SPT with an extra Z$$_2^T$$ symmetry.

- Authors:

- Publication Date:

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

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

- OSTI Identifier:
- 1572132

- Alternate Identifier(s):
- OSTI ID: 1760187

- Grant/Contract Number:
- AC02-05CH11231

- Resource Type:
- Published Article

- Journal Name:
- Nuclear Physics. B

- Additional Journal Information:
- Journal Name: Nuclear Physics. B Journal Volume: 949 Journal Issue: C; Journal ID: ISSN 0550-3213

- Publisher:
- Elsevier

- Country of Publication:
- Netherlands

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

### Citation Formats

```
Tsui, Lokman, Huang, Yen-Ta, and Lee, Dung-Hai. A holographic theory for the phase transitions between fermionic symmetry-protected topological states. Netherlands: N. p., 2019.
Web. doi:10.1016/j.nuclphysb.2019.114799.
```

```
Tsui, Lokman, Huang, Yen-Ta, & Lee, Dung-Hai. A holographic theory for the phase transitions between fermionic symmetry-protected topological states. Netherlands. doi:https://doi.org/10.1016/j.nuclphysb.2019.114799
```

```
Tsui, Lokman, Huang, Yen-Ta, and Lee, Dung-Hai. Sun .
"A holographic theory for the phase transitions between fermionic symmetry-protected topological states". Netherlands. doi:https://doi.org/10.1016/j.nuclphysb.2019.114799.
```

```
@article{osti_1572132,
```

title = {A holographic theory for the phase transitions between fermionic symmetry-protected topological states},

author = {Tsui, Lokman and Huang, Yen-Ta and Lee, Dung-Hai},

abstractNote = {In an earlier work we developed a holographic theory for the phase transition between bosonic symmetry-protected topological (SPT) states. This paper is a continuation of it. Here we present the holographic theory for fermionic SPT phase transitions. We show that in any dimension d, the critical states of fermionic SPT phase transitions has an emergent Z$_2^T$ symmetry and can be realized on the boundary of a d+1-dimensional bulk SPT with an extra Z$_2^T$ symmetry.},

doi = {10.1016/j.nuclphysb.2019.114799},

journal = {Nuclear Physics. B},

number = C,

volume = 949,

place = {Netherlands},

year = {2019},

month = {12}

}

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DOI: https://doi.org/10.1016/j.nuclphysb.2019.114799

DOI: https://doi.org/10.1016/j.nuclphysb.2019.114799

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Works referenced in this record:

##
Quantum phase transitions between a class of symmetry protected topological states

journal, July 2015

- Tsui, Lokman; Jiang, Hong-Chen; Lu, Yuan-Ming
- Nuclear Physics B, Vol. 896

##
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

##
Discrete spin structures and commuting projector models for two-dimensional fermionic symmetry-protected topological phases

journal, September 2016

- Tarantino, Nicolas; Fidkowski, Lukasz
- Physical Review B, Vol. 94, Issue 11

##
Classification of topological insulators and superconductors in three spatial dimensions

journal, November 2008

- Schnyder, Andreas P.; Ryu, Shinsei; Furusaki, Akira
- Physical Review B, Vol. 78, Issue 19

##
Symmetry-protected topological phases in noninteracting fermion systems

journal, February 2012

- Wen, Xiao-Gang
- Physical Review B, Vol. 85, Issue 8

##
Effects of Interaction on Quantum Spin Hall Insulators

journal, October 2011

- Lee, Dung-Hai
- Physical Review Letters, Vol. 107, Issue 16

##
Edge Quantum Criticality and Emergent Supersymmetry in Topological Phases

journal, September 2017

- Li, Zi-Xiang; Jiang, Yi-Fan; Yao, Hong
- Physical Review Letters, Vol. 119, Issue 10

##
Emergent Space-Time Supersymmetry at the Boundary of a Topological Phase

journal, April 2014

- Grover, T.; Sheng, D. N.; Vishwanath, A.
- Science, Vol. 344, Issue 6181

##
Entanglement Spectrum of Topological Insulators and Superconductors

journal, April 2010

- Fidkowski, Lukasz
- Physical Review Letters, Vol. 104, Issue 13

##
General Relationship between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States

journal, May 2012

- Qi, Xiao-Liang; Katsura, Hosho; Ludwig, Andreas W. W.
- Physical Review Letters, Vol. 108, Issue 19

##
Geometric proof of the equality between entanglement and edge spectra

journal, July 2012

- Swingle, Brian; Senthil, T.
- Physical Review B, Vol. 86, Issue 4