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Entanglement Growth and Minimal Membranes in (d+1) Random Unitary Circuits
Piotr Sierant1, Marco Schirò2, Maciej Lewenstein1
1ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain.
Abstract:
Understanding the nature of entanglement growth in many-body systems is one of the fundamental questions in quantum physics. Here, we study this problem by characterizing the entanglement fluctuations and distribution of a (d+1)-dimensional qubit lattice evolved under a random unitary circuit. Focusing on Clifford gates, we perform extensive numerical simulations of random circuits in 1≤d≤4 dimensions. Our findings demonstrate that properties of growth of bipartite entanglement entropy are characterized by the roughening exponents of a d-dimensional membrane in a (d+1)-dimensional elastic medium.
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