Diffusive Operator Spreading for Random Unitary Free Fermion Circuits

2021/02/19 by Beatriz Dias, Masudul Haque, Dias, Beatriz C. +5 · 3 citations
Mathematics · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el)

paper · pdf · doi:10.48550/arxiv.2102.09846

openalex publication_date 2021/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ∼√(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.

Cited by

• Disentangling strategies and entanglement transitions in unitary circuit games with matchgates
• Quadratic Hamiltonian approach to heat transport in fermionic systems
• Entanglement dynamics and Page curves in random permutation circuits

Related

• Operator growth in random quantum circuits with symmetry
• Disorder-enhanced compressibility of Floquet random quantum circuits
• ν-QSSEP: A toy model for entanglement spreading in stochastic diffusive quantum systems
• Quantum complexity and localization in random and time-periodic unitary circuits
• Unusual Diffusivity in Strongly Disordered Quantum Lattices: Random Dimer Model