@article {ISI:000475499200001,
title = {Universal level statistics of the out-of-time-ordered operator},
journal = {Phys. Rev. B},
volume = {100},
number = {3},
year = {2019},
month = {JUL 15},
pages = {035112},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {The out-of-time-ordered correlator has been proposed as an indicator of chaos in quantum systems due to its simple interpretation in the semiclassical limit. In particular, its rate of possible exponential growth at h -> 0 is closely related to the classical Lyapunov exponent. Here we explore how this approach to quantum chaos relates to the random-matrix theoretical description. To do so, we introduce and study the level statistics of the logarithm of the out-of-time-ordered operator, (Lambda) over cap (t) = In (-{[}(x) over cap (t),(p) over cap (x)(0)](2) )/(2t), that we dub the {\textquoteleft}{\textquoteleft}Lyapunovian{{\textquoteright}{\textquoteright}} or {\textquoteleft}{\textquoteleft}Lyapunov operator{{\textquoteright}{\textquoteright}} for brevity. The Lyapunovian{\textquoteright}s level statistics is calculated explicitly for the quantum stadium billiard. It is shown that in the bulk of the filtered spectrum, this statistics perfectly aligns with the Wigner-Dyson distribution. One of the advantages of looking at the spectral statistics of this operator is that it has a well-defined semiclassical limit where it reduces to the matrix of uncorrelated classical finite-time Lyapunov exponents in a partitioned phase space. We provide a heuristic picture interpolating these two limits using Moyal quantum mechanics. Our results show that the Lyapunov operator may serve as a useful tool to characterize quantum chaos and in particular quantum-to-classical correspondence in chaotic systems by connecting the semiclassical Lyapunov growth at early times, when the quantum effects are weak, to universal level repulsion that hinges on strong quantum interference effects.},
issn = {2469-9950},
doi = {10.1103/PhysRevB.100.035112},
author = {Rozenbaum, Efim B. and Ganeshan, Sriram and Galitski, Victor}
}
@article {ISI:000400772100005,
title = {Exactly soluble model of boundary degeneracy},
journal = {PHYSICAL REVIEW B},
volume = {95},
number = {4},
year = {2017},
month = {JAN 25},
abstract = {We investigate the topological degeneracy that can be realized in Abelian fractional quantum spin Hall states with multiply connected gapped boundaries. Such a topological degeneracy (also dubbed as {\textquoteleft}{\textquoteleft}boundary degeneracy{{\textquoteright}{\textquoteright}}) does not require superconducting proximity effect and can be created by simply applying a depletion gate to the quantum spin Hall material and using a generic spin-mixing term (e.g., due to backscattering) to gap out the edge modes. We construct an exactly soluble microscopic model manifesting this topological degeneracy and solve it using the recently developed technique {[}S. Ganeshan and M. Levin, Phys. Rev. B 93, 075118 (2016)]. The corresponding string operators spanning this degeneracy are explicitly calculated. It is argued that the proposed scheme is experimentally reasonable.},
issn = {2469-9950},
doi = {10.1103/PhysRevB.95.045309},
author = {Ganeshan, Sriram and Gorshkov, Alexey V. and Gurarie, Victor and Galitski, Victor M.}
}
@article {6621,
title = {Lyapunov Exponent and Out-of-Time-Ordered Correlator{\textquoteright}s Growth Rate in a Chaotic System},
journal = {Phys. Rev. Lett.},
volume = {118},
year = {2017},
month = {Feb},
pages = {086801},
doi = {10.1103/PhysRevLett.118.086801},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.118.086801},
author = {Rozenbaum, Efim B. and Ganeshan, Sriram and Galitski, Victor}
}
@article {ISI:000404978900007,
title = {Many-body localization in incommensurate models with a mobility edge},
journal = {ANNALEN DER PHYSIK},
volume = {529},
number = {7},
year = {2017},
month = {JUL},
pages = {1600399},
publisher = {WILEY-V C H VERLAG GMBH},
type = {Review},
abstract = {We review the physics of many-body localization in models with incommensurate potentials. In particular, we consider one-dimensional quasiperiodic models with single-particle mobility edges. A conventional perspective suggests that delocalized states act as a thermalizing bath for the localized states in the presence of of interactions. However, contrary to this intuition there is evidence that such systems can display non-ergodicity. This is in part due to the fact that the delocalized states do not have any kind of protection due to symmetry or topology and are thus susceptible to localization. A study of such incommensurate models, in the non-interacting limit, shows that they admit extended, partially extended, and fully localized many-body states. Non-interacting incommensurate models cannot thermalize dynamically and remain localized upon the introduction of interactions. In particular, for a certain range of energy, the system can host a non-ergodic extended (i.e. metallic) phase in which the energy eigenstates violate the eigenstate thermalization hypothesis (ETH) but the entanglement entropy obeys volume-law scaling. The level statistics and entanglement growth also indicate the lack of ergodicity in these models. The phenomenon of localization and non-ergodicity in a system with interactions despite the presence of single-particle delocalized states is closely related to the so-called many-body proximity effect and can also be observed in models with disorder coupled to systems with delocalized degrees of freedom. Many-body localization in systems with incommensurate potentials (without single-particle mobility edges) have been realized experimentally, and we show how this can be modified to study the the effects of such mobility edges. Demonstrating the failure of thermalization in the presence of a single-particle mobility edge in the thermodynamic limit would indicate a more robust violation of the ETH.}, \%\%Address = {POSTFACH 101161, 69451 WEINHEIM, GERMANY},
issn = {0003-3804},
doi = {10.1002/andp.201600399},
author = {Deng, Dong-Ling and Ganeshan, Sriram and Li, Xiaopeng and Modak, Ranjan and Mukerjee, Subroto and Pixley, J. H.}
}
@article { ISI:000381399500005,
title = {Dynamical many-body localization in an integrable model},
journal = {PHYSICAL REVIEW B},
volume = {94},
number = {8},
year = {2016},
month = {AUG 11},
pages = {085120},
issn = {2469-9950},
doi = {10.1103/PhysRevB.94.085120},
author = {Keser, Aydin Cem and Ganeshan, Sriram and Refael, Gil and Galitski, Victor}
}
@article { ISI:000369727700005,
title = {Formalism for the solution of quadratic Hamiltonians with large cosine terms},
journal = {PHYSICAL REVIEW B},
volume = {93},
number = {7},
year = {2016},
month = {FEB 8},
issn = {2469-9950},
doi = {10.1103/PhysRevB.93.075118},
author = {Ganeshan, Sriram and Levin, Michael}
}
@article { ISI:000376908700003,
title = {Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge},
journal = {PHYSICAL REVIEW B},
volume = {93},
number = {18},
year = {2016},
month = {MAY 31},
pages = {184204},
issn = {2469-9950},
doi = {10.1103/PhysRevB.93.184204},
author = {Li, Xiaopeng and Pixley, J. H. and Deng, Dong-Ling and Ganeshan, Sriram and S. Das Sarma}
}
@article {ISI:000352196700010,
title = {Constructing a Weyl semimetal by stacking one-dimensional topological phases},
journal = {PHYSICAL REVIEW B},
volume = {91},
number = {12},
year = {2015},
month = {MAR 30},
pages = {125438},
issn = {1098-0121},
doi = {10.1103/PhysRevB.91.125438},
author = {Ganeshan, Sriram and S. Das Sarma}
}
@article { ISI:000363507300007,
title = {Many-Body Localization and Quantum Nonergodicity in a Model with a Single-Particle Mobility Edge},
journal = {PHYSICAL REVIEW LETTERS},
volume = {115},
number = {18},
year = {2015},
month = {OCT 28},
pages = {186601},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.115.186601},
author = {Li, Xiaopeng and Ganeshan, Sriram and Pixley, J. H. and S. Das Sarma}
}
@article {ISI:000352472400008,
title = {Nearest Neighbor Tight Binding Models with an Exact Mobility Edge in One Dimension},
journal = {PHYSICAL REVIEW LETTERS},
volume = {114},
number = {14},
year = {2015},
month = {APR 9},
pages = {146601},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.114.146601},
author = {Ganeshan, Sriram and Pixley, J. H. and S. Das Sarma}
}
@article { ISI:000341661600003,
title = {Critical integer quantum Hall topology and the integrable Maryland model as a topological quantum critical point},
journal = {PHYSICAL REVIEW B},
volume = {90},
number = {4},
year = {2014},
month = {JUL 11},
issn = {1098-0121},
doi = {10.1103/PhysRevB.90.041405},
author = {Ganeshan, Sriram and Kechedzhi, K. and S. Das Sarma}
}
@article { ISI:000325362500001,
title = {Exact Classification of Landau-Majorana-Stuckelberg-Zener Resonances by Floquet Determinants},
journal = {Phys. Rev. Lett.},
volume = {111},
number = {13},
year = {2013},
month = {SEP 25},
pages = {130405},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.111.130405},
author = {Ganeshan, Sriram and Barnes, Edwin and S. Das Sarma}
}
@article {ISI:000319019300001,
title = {Topological Zero-Energy Modes in Gapless Commensurate Aubry-Andre-Harper Models},
journal = {Phys. Rev. Lett.},
volume = {110},
number = {18},
year = {2013},
month = {may},
pages = {180403},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.110.180403},
author = {Ganeshan, Sriram and Kai Sun and S. Das Sarma}
}