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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; UMass Amherst
  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) (SC-22); 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, Journal Name: Physical Review B Journal Issue: 13 Vol. 100; ISSN 2469-9950; ISSN PRBMDO
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Critical Properties of the Many-Body Localization Transition text January 2016
Scaling Theory of Entanglement at the Many-Body Localization Transition text January 2017
Holographic coherent states from random tensor networks text January 2017
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Cited By (7)

Barrier from chaos: operator entanglement dynamics of the reduced density matrix journal December 2019
Critical properties of the measurement-induced transition in random quantum circuits journal February 2020
Theory of the phase transition in random unitary circuits with measurements journal March 2020
Measurement-induced criticality in random quantum circuits journal March 2020
Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations journal January 2020
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