Title: Entanglement transitions from holographic random tensor networks

Abstract

Here, we introduce a class of phase transitions separating quantum states with different entanglement features. An example of such an “entanglement phase transition” is provided by the many-body localization transition in disordered quantum systems, as it separates highly entangled thermal states at weak disorder from many-body localized states with low entanglement at strong disorder. In the spirit of random matrix theory, we describe a simple model for such transitions where a physical quantum many-body system lives at the “holographic” boundary of a bulk random tensor network. Using a replica trick approach, we map the calculation of the entanglement properties of the boundary system onto the free energy cost of fluctuating domain walls in a classical statistical mechanics model. This allows us to interpret transitions between volume-law and area-law scaling of entanglement as ordering transitions in this statistical mechanics model. Our approach allows us to get an analytic handle on the field theory of these entanglement transitions.

Authors:

Vasseur, Romain ^[1]; Potter, Andrew C. ^[2]; You, Yi-Zhuang ^[3]; Ludwig, Andreas W. W. ^[4]

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+ Show Author Affiliations

1. Univ. of Massachusetts, Amherst, MA (United States). Dept. of Physics
2. Univ. of Texas, Austin, TX (United States). Dept. of Physics
3. Harvard Univ., Cambridge, MA (United States). Dept. of Physics; Univ. of California, San Diego, CA (United States). Dept. of Physics
4. Univ. of California, Santa Barbara, CA (United States). Dept. of physics

Publication Date:

2019-10-09

Research Org.:

Univ. of Massachusetts, Amherst, MA (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division

OSTI Identifier:

1569745

Grant/Contract Number:  

SC0019168

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review B

Additional Journal Information:

Journal Volume: 100; Journal Issue: 13; Journal ID: ISSN 2469-9950

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Quantum entanglement; tensor networks