1:30 pm MCP 201
Measurement-indeed criticality in random quantum circuits
Chaoming Jian, Microsoft Station Q
Abstract: In this talk, I will present the study of the critical behavior of the entanglement transition induced by projective measurements in (Haar) random unitary quantum circuits. I will present a replica approach that maps 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. I will discuss the general scaling properties of the entanglement entropies and mutual information near the transition using conformal invariance. I will focus on a more detailed analysis in the limit of infinite on-site Hilbert space dimension in which the statistical mechanics model maps onto percolation. In particular, this analysis yields the exact value of the universal coefficient of the logarithm of subsystem size in the Rényi (including Von Neumann) entropies. I also will 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.