# 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: P34.00012 : Structure of the Entanglement Entropy of (3+1)D Gapped Phases of Matter

5:06 PM–5:18 PM

#### Presenter:

Yunqin Zheng

(Physics Department, Princeton Univ)

#### Authors:

Yunqin Zheng

(Physics Department, Princeton Univ)

Huan He

(Physics Department, Princeton Univ)

Barry Bradlyn

(Princeton Center for Theoretical Science, Princeton University)

Jennifer Cano

(Princeton Center for Theoretical Science, Princeton University)

Titus Neupert

(Department of Physics, University of Zurich)

Andrei Bernevig

(Physics Department, Princeton Univ)

We study the entanglement entropy of gapped phases of matter in three spatial dimensions. We focus in particular on size-independent contributions to the entropy across entanglement surfaces of arbitrary topologies. We show that for low energy fixed-point theories, the constant part of the entanglement entropy across any surface can be reduced to a linear combination of the entropies across a sphere and a torus. We first derive the constant part of the entanglement entropy of the fixed-point models across arbitrary entanglement surfaces, and identify the topological contribution by considering the renormalization group flow; in this way we give an explicit definition of topological entanglement entropy in (3+1)D, which sharpens previous results. We illustrate our results using several concrete examples and independent calculations, and show adding ``twist'' terms to the Lagrangian can change $S_{\mathrm{topo}}$ in (3+1)D. For the generalized Walker-Wang models, we find that the ground state degeneracy on a 3-torus is given by $\exp(-3S_{\mathrm{topo}}[T^2])$ in terms of the topological entanglement entropy across a 2-torus.

## 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