A long period of linear growth in the spectral form factor provides a universal diagnostic of quantum chaos at intermediate times. By contrast, the behavior of the spectral form factor in disordered integrable many-body models is not well understood. Here we study the two-body Sachdev-Ye-Kitaev model and show that the spectral form factor features an exponential ramp, in sharp contrast to the linear ramp in chaotic models. We find a novel mechanism for this exponential ramp in terms of a high-dimensional manifold of saddle points in the path integral formulation of the spectral form factor. This manifold arises because the theory enjoys a large symmetry group. With finite nonintegrable interaction strength, these delicate symmetries reduce to a relative time translation, causing the exponential ramp to give way to a linear ramp.

}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.125.250602}, author = {Winer, Michael and Jian, Shao-Kai and Swingle, Brian} } @article { ISI:000571399800001, title = {Minimal Model for Fast Scrambling}, journal = {Phys. Rev. Lett.}, volume = {125}, number = {13}, year = {2020}, month = {SEP 21}, pages = {130601}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We study quantum information scrambling in spin models with both long-range all-to-all and shortrange interactions. WC argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give rise to fast scrambling, which describes the spread of quantum information over the entire system in a time that is logarithmic in the system size. This is illustrated in two tractable models: (1) a random circuit with Haar random local unitaties and a global interaction and (2) a classical model of globally coupled nonlinear oscillators. We use exact numerics to provide further evidence by studying the time evolution of an out-of-time-order correlator and entanglement entropy in spin chains of intermediate sizes. Our results pave the way towards experimental investigations of fast scrambling and aspects of quantum gravity with quantum simulators.}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.125.130601}, author = {Belyansky, Ron and Bienias, Przemyslaw and Kharkov, Yaroslav A. and Gorshkov, V, Alexey and Swingle, Brian} } @article {yoo_nonequilibrium_2020, title = {Nonequilibrium steady state phases of the interacting {Aubry}-{Andre}-{Harper} model}, journal = {Phys. Rev. B}, volume = {102}, number = {19}, year = {2020}, note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article}, month = {nov}, abstract = {Here, we study the phase diagram of the Aubry-Andre-Harper model in the presence of strong interactions as the strength of the quasiperiodic potential is varied. Previous work has established the existence of a many-body localized phase at a large potential strength; here, we find a rich phase diagram in the delocalized regime characterized by spin transport and unusual correlations. We calculate the nonequilibrium steady states of a boundary-driven strongly interacting Aubry-Andre-Harper model by employing the time-evolving block decimation algorithm on matrix product density operators. From these steady states, we extract spin transport as a function of system size and quasiperiodic potential strength. These data show spin transport going from superdiffusive to subdiffusive well before the localization transition; comparing to previous results, we also find that the transport transition is distinct from a transition observed in the speed of operator growth in the model. We also investigate the correlation structure of the steady state and find an unusual oscillation pattern for intermediate values of the potential strength. The unusual spin transport and quantum correlation structure suggest multiple dynamical phases between the much-studied thermal and many-body localized phases.}, issn = {2469-9950}, doi = {10.1103/PhysRevB.102.195142}, author = {Yoo, Yongchan and Lee, Junhyun and Swingle, Brian} } @article { ISI:000530031700002, title = {Operator Levy Flight: Light Cones in Chaotic Long-Range Interacting Systems}, journal = {Phys. Rev. Lett.}, volume = {124}, number = {18}, year = {2020}, month = {MAY 4}, pages = {180601}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We argue that chaotic power-law interacting systems have emergent limits on information propagation, analogous to relativistic light cones, which depend on the spatial dimension d and the exponent a governing the decay of interactions. Using the dephasing nature of quantum chaos, we map the problem to a stochastic model with a known phase diagram. A linear light cone results for alpha >= d + 1/2. We also provide a Levy flight (long-range random walk) interpretation of the results and show consistent numerical data for 1D long-range spin models with 200 sites.}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.124.180601}, author = {Zhou, Tianci and Xu, Shenglong and Chen, Xiao and Guo, Andrew and Swingle, Brian} } @article {10436, title = {Unscrambling the physics of out-of-time-order correlators}, journal = {Nature Physics}, volume = {14}, year = {2018}, pages = {988{\textendash}990}, abstract = {Quantitative tools for measuring the propagation of information through quantum many-body systems, originally developed to study quantum chaos, have recently found many new applications from black holes to disordered spin systems.

}, isbn = {1745-2481}, doi = {10.1038/s41567-018-0295-5}, url = {https://doi.org/10.1038/s41567-018-0295-5}, author = {Swingle, Brian} } @article { ISI:000358372100002, title = {Proposal to probe quantum nonlocality of Majorana fermions in tunneling experiments}, journal = {PHYSICAL REVIEW B}, volume = {92}, number = {2}, year = {2015}, month = {JUL 22}, issn = {1098-0121}, doi = {10.1103/PhysRevB.92.020511}, author = {Sau, Jay D. and Swingle, Brian and Tewari, Sumanta} }