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Void formation in operator growth, entanglement, and unitarity · Around

2019

Void formation in operator growth, entanglement, and unitarity

Liu, Hong, Vardhan, Shreya

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The structure of the Heisenberg evolution of operators plays a key role in explaining diverse processes in quantum many-body systems.

In this paper, we discuss a new universal feature of operator evolution: an operator can develop a void during its evolution, where its nontrivial parts become separated by a region of identity operators.
Such processes are present in both integrable and chaotic systems, and are required by unitarity.
We show that void formation has important implications for unitarity of entanglement growth and generation of mutual information and multipartite entanglement.

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S. Gopalakrishnan, D. A. Huse, V. Khemani, and R. Vasseur, “Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems,” arXiv:1809.02126
Original
1912
Earlier work this paper cites.
E. H. Lieb and D. W. Robinson, “The finite group velocity of quantum spin systems,” Commun. Math. Phys
1972
Earlier work this paper cites.
P. Calabrese and J. L. Cardy, “Evolution of entanglement entropy in one-dimensional systems,” J. Stat. Mech. 0504
2005
Earlier work this paper cites.
T. Prosen and I. Piorn, “Operator space entanglement entropy in transverse Ising chain” Phys. Rev
Original
2007
Earlier work this paper cites.
D. M. Schlingemann, H. Vogts, and R. F. Werner, Journal of Mathematical Physics
2008
Earlier work this paper cites.
I. Piorn and T. Prosen , “Operator Space Entanglement Entropy in XY Spin Chains” Phys. Rev
Original
2009
Earlier work this paper cites.

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