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arXiv · 2306.04764

Entanglement Growth and Minimal Membranes in $(d+1)$ Random Unitary Circuits

Piotr Sierant·Marco Schirò·Maciej Lewenstein·Xhek Turkeshi
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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 $(d+1)$ qubit lattice evolved under a random unitary circuit. Focusing on Clifford gates, we perform extensive numerical simulations of random circuits in $1\le d\le 4$ 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 $(d+1)$ elastic medium.

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Piotr Sierant, Marco Schirò, Maciej Lewenstein, Xhek Turkeshi. 2023-06-07. Entanglement Growth and Minimal Membranes in $(d+1)$ Random Unitary Circuits. https://doi.org/10.1103/physrevlett.131.230403

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