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Universal Logarithmic Scrambling in Many Body Localization
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abstract
Out of time ordered correlator (OTOC) is recently introduced as a powerful diagnose for quantum chaos. To go beyond, here we present an analytical solution of OTOC for a non-chaotic many body localized (MBL) system, showing distinct feature from quantum chaos and Anderson localization (AL). The OTOC is found to fall only if the nearest distance between the two operators being shorter than $\xi\ln t$, where $\xi$ is dimensionless localization length. Thereafter, we found an universal power law decay of OTOC as $2^{-\xi\ln t}$, implying an universal logarithmic growth of second R\'{e}nyi entropy, where $\xi$ plays the role of information scrambling rate. A relation between butterfly velocity and scrambling rate is found.
Forward citations
Cited by 4 Pith papers
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Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport
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Operator delocalization in disordered spin chains via exact MPO marginals
For the disordered XXZ chain, the Pauli-basis operator length, computed exactly from MPO marginals, grows logarithmically in the interacting MBL regime and saturates in the Anderson-localized case.
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Quantum information scrambling in strongly disordered Rydberg spin systems
In strongly disordered XXZ spin chains, power-law interactions produce algebraic OTOC light cones rather than the logarithmic ones of nearest-neighbor many-body localization, even for short-range van der Waals coupling.
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Post-Selection Probability and Fidelity of Bidirectional Teleportation
Post-selection probability and fidelity of bidirectional teleportation are expressed via the Loschmidt echo, revealing initial-state dependence of fidelity and stability of probability in integrable models.
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