Out‐of‐time‐order correlations in many‐body localized and thermal phases
By Xiao Chen, Tianci Zhou, D. Huse, E. Fradkin. 2016
171 citations recorded by the source corpus.
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, and show that their amplitudes after disorder averaging approach their long‐time limits as power‐laws of time. This power‐law dynamics is due to dephasing caused by interactions between the localized operators that fall off exponentially with distance. The long‐time limits of the OTO correlators are determined by the overlaps of the local operators with the conserved l‐bits. We demonstrate numerically our results in the effective model and three other more “realistic” spin chain models. Furthermore, we extend our calculations to the thermal phase and find that for a time‐independent Hamiltonian, the OTO correlators also appear to vanish as a power law at long time, perhaps due to coupling to conserved densities. In contrast, we find that in the thermal phase of a Floquet spin model with no conserved densities the OTO correlator decays exponentially at long times.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/93059b1ed2bb643fb3e6efcc12408265109b8f44
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In Atomic and Molecular Physics, and Optics
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Citations in the corpus
- Onset of many-body chaos in the $O(N)$ model (2017, background): “At the other extreme, disordered quantum systems typically scramble much more slowly than their clean counterparts [22] [23] [24] [25] [26] [27].”
- Many-body localization: An introduction and selected topics (2017, unknown): “While there have been important pioneer experiments [211,212], the experimental determination of entanglement dynamics in a scalable two different locations in the system (non-local spin-echo spin-echo protocol) could pick up the weak interaction between the lioms, resulting in different signals for”
- Diffusive Hydrodynamics of Out-of-Time-Ordered Correlators with Charge Conservation (2017, background): “Our random circuit predictions also help in explaining existing numerical results in timeindependent ergodic spin chains [36].”
- Measurement-driven entanglement transition in hybrid quantum circuits (2019, background): “As for unitary Hamiltonian dynamics, there is a notion of chaos in such Floquet circuits, as diagnosed by the entanglement growth [49,50], the operator growth (and butterfly effect in out-oftime-order correlator) [51], the level spacing statistics and the spectral form factor [45,46,48,52], etc.”
- Colloquium : Many-body localization, thermalization, and entanglement (2018, background): “In addition, power-law decays of various quantities due to the same mechanism have been identified, including mutual information (De Tomasi et al., 2017), fluctuations of the out-of-time correlation functions (Chen et al., 2016) and fluctuations of the Loschmidt echo (Serbyn and Abanin, 2017).”
- Time-evolution methods for matrix-product states (2019, background): “emostsuitablewhile forshorttimes,anyofthemethodsworkreasonablywell. 8.4. OTOCsforinteractingspins Thefinalexampleismotivatedbythestudyofinformationspreadingandscramblinginclosedquantum many-bodysystems[74,81,82]. Thiscanbedonebystudyingthedynamicsofout-of-time-ordercorrelators (OTOCs)oflocalobservabl”
- Random Quantum Circuits (2022, methodology): “The OTOC has been used to diagnose the scrambling of locally-accessible quantum information (165, 166, 167), and its growth in time provides signatures of key properties of quantum many-body systems, including their chaotic (128, 168, 169, 170), disordered (171, 147, 172, 173, 174, 175, 176), or int”
- Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos (2018, methodology): “by either a time-independent Hamiltonian[19, 21–24, 29– 39], or by Floquet dynamics[40, 41], or by a random unitary circuit [18, 42–46].”