@article{b1433236cbb642bd8982cfdeb7d0c000,
title = "Critical properties of the measurement-induced transition in random quantum circuits",
abstract = "We numerically study the measurement-driven quantum phase transition of Haar-random quantum circuits in 1+1 dimensions. By analyzing the tripartite mutual information we are able to make a precise estimate of the critical measurement rate pc=0.17(1). We extract estimates for the associated bulk critical exponents that are consistent with the values for percolation, as well as those for stabilizer circuits, but differ from previous estimates for the Haar-random case. Our estimates of the surface order parameter exponent appear different from those for stabilizer circuits or percolation, but we cannot definitively rule out the scenario where all exponents in the three cases match. Moreover, in the Haar case the prefactor for the entanglement entropies Sn depends strongly on the R{\'e}nyi index n; for stabilizer circuits and percolation this dependence is absent. Results on stabilizer circuits are used to guide our study and identify measures with weak finite-size effects. We discuss how our numerical estimates constrain theories of the transition.",
author = "Aidan Zabalo and Gullans, {Michael J.} and Wilson, {Justin H.} and Sarang Gopalakrishnan and Huse, {David A.} and Pixley, {J. H.}",
note = "Funding Information: Acknowledgments . We thank Ehud Altman, Soonwon Choi, Vedika Khemani, Andreas Ludwig, Adam Nahum, Xiaoliang Qi, Jonathan Ruhman, Brian Skinner, and Romain Vasseur for helpful discussions. A.Z. is partially supported through a Fellowship from the Rutgers Discovery Informatics Institute. M.G. and D.H. are supported in part by the DARPA DRINQS program. S.G. acknowledges support from NSF Grant No. DMR-1653271. D.H. is also supported in part by a Simons Fellowship. J.H.P. is partially supported by Grant No. 2018058 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel. S.G. and J.H.P. initiated this work at the Kavli Institute for Theoretical Physics, which is supported by NSF Grant No. PHY-1748958, and J.H.W, S.G. and J.H.P. performed part of this work at the Aspen Center for Physics, which is supported by NSF Grant No. PHY- 1607611. The authors acknowledge the Beowulf cluster at the Department of Physics and Astronomy of Rutgers University, the Office of Advanced Research Computing (OARC) at Rutgers, The State University of New Jersey [35] for providing access to the Amarel cluster, the Rutgers Discovery Informatics Institute for providing access to the Caliburn [36] cluster supported by Rutgers and the State of New Jersey, and associated research computing resources that have contributed to the results reported here. Publisher Copyright: {\textcopyright} 2020 American Physical Society.",
year = "2020",
month = feb,
day = "1",
doi = "10.1103/PhysRevB.101.060301",
language = "English (US)",
volume = "101",
journal = "Physical Review B",
issn = "2469-9950",
publisher = "American Physical Society",
number = "6",
}