# Bulletin of the American Physical Society

# APS March Meeting 2018

## Monday–Friday, March 5–9, 2018; Los Angeles, California

### Session P34: Machine Learning in Condensed Matter Physics III

2:30 PM–5:18 PM,
Wednesday, March 7, 2018

LACC
Room: 409A

Sponsoring
Units:
DCOMP DCMP

Chair: Simon Trebst, Univ Cologne

### Abstract: P34.00011 : Entanglement Entropy From Tensor Network States for Stabilizer Codes

4:54 PM–5:06 PM

#### Presenter:

Huan He

(Physics, Princeton University)

#### Authors:

Huan He

(Physics, Princeton University)

Yunqin Zheng

(Physics, Princeton University)

Andrei Bernevig

(Physics, Princeton University)

Nicolas Regnault

(Laboratoire Pierre Aigrain, Ecole Normale Superieure Paris)

We present the construction of tensor network states (TNS) for some of the degenerate ground states of 3D stabilizer codes, and use the TNS formalism to obtain the entanglement spectrum and entropy of these ground-states for some special cuts. In particular, we work out the examples of the 3D toric code, the X-cube model and the Haah code. The latter two models belong to the category of "fracton" models proposed recently, while the first one belongs to the conventional topological phases. We mention the cases for which the entanglement entropy and spectrum can be calculated exactly: for these, the constructed TNS is the singular value decomposition (SVD) of the ground states with respect to particular entanglement cuts. Apart from the area law, the entanglement entropies also have constant and linear corrections for the fracton models, while the entanglement entropies for the toric code models only have constant corrections. For the cuts we consider, the entanglement spectra of these three models are completely flat. We also conjecture that the negative linear correction to the area law is a signature of extensive ground state degeneracy. We show that the transfer matrices are projectors. The number of nonzero eigenvalues is tightly related to the ground state degeneracy.

## Follow Us |
## Engage
Become an APS Member |
## My APS
Renew Membership |
## Information for |
## About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |

© 2018 American Physical Society
| All rights reserved | Terms of Use
| Contact Us

**Headquarters**
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200

**Editorial Office**
1 Research Road, Ridge, NY 11961-2701
(631) 591-4000

**Office of Public Affairs**
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700