Out-of-time ordered correlators and entanglement growth in the random-field XX spin chain

@article{Riddell2019OutoftimeOC,
  title={Out-of-time ordered correlators and entanglement growth in the random-field XX spin chain},
  author={Jonathon Riddell and Erik S. S{\o}rensen},
  journal={Physical Review B},
  year={2019}
}
We study out of time order correlations, $C(x,t)$ and entanglement growth in the random field XX model with open boundary conditions using the exact Jordan-Wigner transformation to a fermionic Hamiltonian. For any non-zero strength of the random field this model describes an Anderson insulator. Two scenarios are considered: A global quench with the initial state corresponding to a product state of the Neel form, and the behaviour in a typical thermal state at $\beta=1$. As a result of the… Expand
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References

SHOWING 1-10 OF 104 REFERENCES
Slow Growth of Out-of-Time-Order Correlators and Entanglement Entropy in Integrable Disordered Systems.
TLDR
It is demonstrated that out-of-time-order correlators can spread slowly beyond the single-particle localization length, despite the absence of many-body interactions, and argued that this nonlocality becomes relevant for time-dependent correlation functions. Expand
Out-of-Time-Ordered Density Correlators in Luttinger Liquids.
Information scrambling and the butterfly effect in chaotic quantum systems can be diagnosed by out-of-time-ordered (OTO) commutators through an exponential growth and large late time value. We showExpand
Out-of-time-ordered correlators in a quantum Ising chain
Out-of-time-ordered correlators (OTOC) have been proposed to characterize quantum chaos in generic systems. However, they can also show interesting behavior in integrable models, resembling the OTOCExpand
Information propagation in isolated quantum systems
Entanglement growth and out-of-time-order correlators (OTOC) are used to assess the propagation of information in isolated quantum systems. In this work, using large scale exact time-evolution weExpand
Universal slow growth of entanglement in interacting strongly disordered systems.
TLDR
This work shows that the logarithmic entanglement growth is a universal phenomenon characteristic of the many-body localized phase in any number of spatial dimensions, and reveals a broad hierarchy of dephasing time scales present in such a phase. Expand
Out-of-Time-Order Correlation in Marginal Many-Body Localized Systems
We show that the out-of-time-order correlation (OTOC) $ \langle W(t)^\dagger V(0)^\dagger W(t)V(0)\rangle$ in many-body localized (MBL) and marginal MBL systems can be efficiently calculated by theExpand
Diffusive Hydrodynamics of Out-of-Time-Ordered Correlators with Charge Conservation
The scrambling of quantum information in closed many-body systems has received considerable recent attention. Two useful measures of scrambling have emerged: the spreading of initially-localExpand
Out-of-time-order correlations in many-body localized and thermal phases
We use the out-of-time-order (OTO) correlators to study the slow dynamics in the many-body localized (MBL) phase. We investigate OTO correlators in the effective ("l-bit") model of the MBL phase, andExpand
Entanglement entropy dynamics of disordered quantum spin chains
By means of free fermionic techniques we study the time evolution of the entanglement entropy, S(t), of a block of spins in the random transverse-field Ising chain after a sudden change of theExpand
Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws
Thermalization and scrambling are the subject of much recent study from the perspective of many-body quantum systems with locally bounded Hilbert spaces (`spin chains'), quantum field theory andExpand
...
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