Diffusive Operator Spreading for Random Unitary Free Fermion Circuits

• URL: http://arxiv.org/abs/2102.09846v1
• Date: Fri, 19 Feb 2021 10:31:27 GMT
• Title: Diffusive Operator Spreading for Random Unitary Free Fermion Circuits
• Authors: Beatriz C. Dias, Masudul Haque, Pedro Ribeiro, Paul McClarty
• Abstract summary: We study a model of free fermions on a chain with dynamics generated by random unitary gates on nearest neighbor bonds. In all three cases, temporal disorder causes diffusive operator spreading and $simstt$ entanglement growth. This is in sharp contrast to Anderson localization for the case of static disorder and with the ballistic behavior observed in both the clean case of Hamiltonian evolution and in fully random unitary quantum circuits.
• Score: 0.9290757451344674
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study a model of free fermions on a chain with dynamics generated by random unitary gates acting on nearest neighbor bonds and present an exact calculation of time-ordered and out-of-time-ordered correlators. We consider three distinct cases: the random circuit with spatio-temporal disorder (i) with and (ii) without particle number conservation and (iii) the particle non-conserving case with purely temporal disorder. In all three cases, temporal disorder causes diffusive operator spreading and $\sim\sqrt{t}$ entanglement growth. This is in sharp contrast to Anderson localization for the case of static disorder and with the ballistic behavior observed in both the clean case of Hamiltonian evolution and in fully random unitary quantum circuits.

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