Absence of localization in two-dimensional Clifford circuits

• URL: http://arxiv.org/abs/2210.10129v2
• Date: Fri, 5 May 2023 20:26:31 GMT
• Title: Absence of localization in two-dimensional Clifford circuits
• Authors: Tom Farshi, Jonas Richter, Daniele Toniolo, Arijeet Pal, Lluis Masanes
• Abstract summary: We analyze a Floquet circuit with random Clifford gates in one and two spatial dimensions. By using random graphs and methods from percolation theory, we prove in the two dimensional setting that some local operators grow at ballistic rate. In contrast, the one-dimensional model displays a strong form of localization characterized by the emergence of left and right-blocking walls in random locations.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We analyze a Floquet circuit with random Clifford gates in one and two spatial dimensions. By using random graphs and methods from percolation theory, we prove in the two dimensional setting that some local operators grow at ballistic rate, which implies the absence of localization. In contrast, the one-dimensional model displays a strong form of localization characterized by the emergence of left and right-blocking walls in random locations. We provide additional insights by complementing our analytical results with numerical simulations of operator spreading and entanglement growth, which show the absence (presence) of localization in two-dimension (one-dimension). Furthermore, we unveil that the spectral form factor of the Floquet unitary in two-dimensional circuits behaves like that of quasi-free fermions with chaotic single particle dynamics, with an exponential ramp that persists till times scaling linearly with the size of the system. Our work sheds light on the nature of disordered, Floquet Clifford dynamics and its relationship to fully chaotic quantum dynamics.

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