# Holographic entropy inequalities and gapped phases of matter

## Abstract

Here, we extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the “cyclic inequalities” derived recently for the holo-graphic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.

- Authors:

- California Inst. of Technology (CalTech), Pasadena, CA (United States). Inst. for Quantum Information and Matter and Walter Burke Inst. for Theoretical Physics
- California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
- Stanford Univ., Stanford, CA (United States). Stanford Inst. for Theoretical Physics

- Publication Date:

- Research Org.:
- California Inst. of Technology, Pasadena, CA (United States)

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

- OSTI Identifier:
- 1455189

- Grant/Contract Number:
- SC0011632

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 9; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Holography and condensed matter physics (AdS/CMT); Topological States of Matter

### Citation Formats

```
Bao, Ning, Cao, ChunJun, Walter, Michael, and Wang, Zitao. Holographic entropy inequalities and gapped phases of matter. United States: N. p., 2015.
Web. doi:10.1007/JHEP09(2015)203.
```

```
Bao, Ning, Cao, ChunJun, Walter, Michael, & Wang, Zitao. Holographic entropy inequalities and gapped phases of matter. United States. doi:10.1007/JHEP09(2015)203.
```

```
Bao, Ning, Cao, ChunJun, Walter, Michael, and Wang, Zitao. Tue .
"Holographic entropy inequalities and gapped phases of matter". United States. doi:10.1007/JHEP09(2015)203. https://www.osti.gov/servlets/purl/1455189.
```

```
@article{osti_1455189,
```

title = {Holographic entropy inequalities and gapped phases of matter},

author = {Bao, Ning and Cao, ChunJun and Walter, Michael and Wang, Zitao},

abstractNote = {Here, we extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the “cyclic inequalities” derived recently for the holo-graphic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.},

doi = {10.1007/JHEP09(2015)203},

journal = {Journal of High Energy Physics (Online)},

number = 9,

volume = 2015,

place = {United States},

year = {2015},

month = {9}

}

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