Understanding the spreading of the operator space entanglement entropy (OSEE) is key in order to explore out-of-equilibrium quantum many-body systems. Here we argue that for integrable models the dynamics of the OSEE is related to the diffusion of the operator front. We derive the logarithmic bound 1/2ln(t) for the OSEE of some simple, i.e., low-rank, diagonal local operators. We numerically check that the bound is saturated in the rule 54 chain, which is representative of interacting integrable systems. Remarkably, the same bound is saturated in the spin-1/2 Heisenberg XXZ chain. Away from the isotropic point and from the free-fermion point, the OSEE grows as 1/2ln(t), irrespective of the chain anisotropy, suggesting universality. Finally, we discuss the effect of integrability breaking. We show that strong finite-time effects are present, which prevent us from probing the asymptotic behavior of the OSEE.

Diffusion and operator entanglement spreading

Alba V.
2021

Abstract

Understanding the spreading of the operator space entanglement entropy (OSEE) is key in order to explore out-of-equilibrium quantum many-body systems. Here we argue that for integrable models the dynamics of the OSEE is related to the diffusion of the operator front. We derive the logarithmic bound 1/2ln(t) for the OSEE of some simple, i.e., low-rank, diagonal local operators. We numerically check that the bound is saturated in the rule 54 chain, which is representative of interacting integrable systems. Remarkably, the same bound is saturated in the spin-1/2 Heisenberg XXZ chain. Away from the isotropic point and from the free-fermion point, the OSEE grows as 1/2ln(t), irrespective of the chain anisotropy, suggesting universality. Finally, we discuss the effect of integrability breaking. We show that strong finite-time effects are present, which prevent us from probing the asymptotic behavior of the OSEE.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/1142273
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