Entanglement transitions from holographic random tensor networks

By Romain Vasseur, Andrew C. Potter, Yi-Zhuang You, A. Ludwig. Physical review B, 2018

175 citations recorded by the source corpus.

Universal features in patterns of entanglement of quantum states provide valuable information-theoretical insights into complex quantum many-body phases and dynamics. This work uncovers a novel class of phase transition between weakly- and strongly- entangled quantum states, described holographically at the boundary of a random tensor network. The univeral scaling structure of these transitions is explored via an exact mapping onto a classical spin model, which also opens the door to efficient numerical methods to study these complex quantum phenomena.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8f52a6bb3f1bbf0386354693e287bb0af1db3f27

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. Matthew Fisher
3. V. Khemani
4. B. Skinner
5. J. Ruhman
6. S. Vijay
7. S. Gopalakrishnan
8. Sthitadhi Roy

In Nuclear and High Energy Physics

1. Matthew Fisher
2. Timothy H. Hsieh
3. Shengqi Sang
4. A. Nahum
5. J. Ruhman
6. B. Skinner
7. S. Vijay
8. Romain Vasseur

In Statistical and Nonlinear Physics

1. A. Nahum
2. J. Ruhman
3. B. Skinner
4. S. Gopalakrishnan
5. V. Khemani
6. Sthitadhi Roy
7. Andrew C. Potter
8. S. Vijay

Citations in the corpus

• Measurement-Induced Phase Transitions in the Dynamics of Entanglement (2018, methodology): “A starting point may be the replica trick, which has been used in unitary circuits and random tensor networks [18, 25] to construct mappings to (replica limits of) effective classical spin models in which the degrees of freedom are permutations [24].”
• Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory (2020, methodology): “[35], for Haar circuits in [33], and for circuits with measurement in Refs.”
• Entanglement and Charge-Sharpening Transitions in U(1) Symmetric Monitored Quantum Circuits (2021, background): “[19, 20] (see also [59, 60] in the context of random tensor networks)”
• Measurement-protected quantum phases (2020, background): “discussed in the context of entanglement transitions in random tensor networks [43].”
• Random Quantum Circuits (2022, methodology): “This is closely connected to the problem of formulating a field theory for the entanglement transition in a random tensor network (RTN) (134) (a random tensor network, with “virtual” bonds in the bulk and “physical” bonds on the boundary, can undergo an entanglement phase transition as a function of”