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Title: Entanglement transitions from holographic random tensor networks

Journal Article · · Physical Review B
 [1];  [2];  [3];  [4]
  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
+ Show Author Affiliations

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.

Research Organization:
Univ. of Massachusetts, Amherst, MA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
Grant/Contract Number:
SC0019168
OSTI ID:
1569745
Journal Information:
Physical Review B, Vol. 100, Issue 13; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 62 works
Citation information provided by
Web of Science

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Many-body localization phase transition: A simplified strong-randomness approximate renormalization group text January 2016
Critical Properties of the Many-Body Localization Transition text January 2016
Scaling Theory of Entanglement at the Many-Body Localization Transition text January 2017
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Cited By (3)

Barrier from chaos: operator entanglement dynamics of the reduced density matrix journal December 2019
Measurement-induced criticality in random quantum circuits text January 2019
Critical properties of the measurement-induced transition in random quantum circuits text January 2019

Figures / Tables (8)

FIG. 1(p. 2)figure FIG. 1
FIG. 2(p. 4)figure FIG. 2
FIG. 3(p. 5)figure FIG. 3
FIG. 4(p. 6)figure FIG. 4
FIG. 5(p. 7)figure FIG. 5
FIG. 6(p. 8)figure FIG. 6
FIG. 7(p. 11)figure FIG. 7
FIG. 8(p. 15)figure FIG. 8

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Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Quantum entanglement
tensor networks