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MEASUREMENT-INDUCED CRITICALITY IN RANDOM QUANTUM CIRCUITS

Oleh   Chao-Ming Jian [-]
Kontributor / Dosen Pembimbing : Yi-Zhuang You, Romain Vasseur, and Andreas W. W. Ludwig
Jenis Koleksi : Jurnal elektronik
Penerbit : FMIPA - Fisika
Fakultas : Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA)
Subjek :
Kata Kunci : -
Sumber : PHYSICAL REVIEW B 101, 104302 (2020), APS
Staf Input/Edit : Ratnasari  
File : 1 file
Tanggal Input : 2020-03-04 15:47:44

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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 nth 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. 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)].

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