Measurement-induced criticality in random quantum circuits

Journal Article · 03 March 2020 · Physical Review B

DOI: https://doi.org/10.1103/PhysRevB.101.104302 · OSTI ID:1603484

Jian, Chao-Ming ^[1]; You, Yi-Zhuang ^[2]; Vasseur, Romain ^[3]; Ludwig, Andreas W. W. ^[4]

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1. Station Q, Microsoft Quantum, Santa Barbara, CA (United States); Univ. of California, Santa Barbara, CA (United States). Kavli Inst. of Theoretical Physics; UMass Amherst
2. Univ. of California, San Diego, CA (United States)
3. Univ. of Massachusetts, Amherst, MA (United States)
4. Univ. of California, Santa Barbara, CA (United States)

We investigate the critical behavior of the entanglement transition induced by projective measurements in (Haar) random unitary quantum circuits. Using a replica approach, we map the calculation of the entanglement entropies in such circuits onto a two-dimensional statistical-mechanics model. In this language, the area- to volume-law entanglement transition can be interpreted as an ordering transition in the statistical-mechanics model. We derive the general scaling properties of the entanglement entropies and mutual information near the transition using conformal invariance. We analyze in detail the limit of infinite on-site Hilbert space dimension in which the statistical-mechanics model maps onto percolation. In particular, we compute the exact value of the universal coefficient of the logarithm of subsystem size in the n th Rényi entropies for n ≥ 1 in this limit using relatively recent results for the conformal field theory describing the critical theory of two-dimensional (2D) percolation, and we discuss how to access the generic transition at finite on-site Hilbert space dimension from this limit, which is in a universality class different from 2D percolation. Here, we also comment on the relation to the entanglement transition in random tensor networks, studied previously in Vasseur et al. [Phys. Rev. B 100, 134203 (2019)].

• Research Organization: Univ. of Massachusetts, Amherst, MA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; National Science Foundation (NSF); Gordon and Betty Moore Foundation (GBMF); Alfred P. Sloan Foundation
• Grant/Contract Number: SC0019168
• OSTI ID: 1603484
• Journal Information: Physical Review B, Journal Name: Physical Review B Journal Issue: 10 Vol. 101; ISSN 2469-9950; ISSN PRBMDO
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English