{
  "id": "1907.01609",
  "version": "v1",
  "published": "2019-07-02T19:56:57.000Z",
  "updated": "2019-07-02T19:56:57.000Z",
  "title": "Intermittency of dynamical phases in a quantum spin glass",
  "authors": [
    "Vadim N. Smelyanskiy",
    "Kostyantyn Kechedzhi",
    "Sergio Boixo",
    "Hartmut Neven",
    "Boris Altshuler"
  ],
  "comment": "16 pages, 12 figures",
  "categories": [
    "cond-mat.dis-nn",
    "quant-ph"
  ],
  "abstract": "Answering the question of existence of efficient quantum algorithms for NP-hard problems require deep theoretical understanding of the properties of the low-energy eigenstates and long-time coherent dynamics in quantum spin glasses. We discovered and described analytically the property of asymptotic orthogonality resulting in a new type of structure in quantum spin glass. Its eigen-spectrum is split into the alternating sequence of bands formed by quantum states of two distinct types ($x$ and $z$). Those of $z$-type are non-ergodic extended eigenstates (NEE) in the basis of $\\{\\sigma_z\\}$ operators that inherit the structure of the classical spin glass with exponentially long decay times of Edwards Anderson order parameter at any finite value of transverse field $B_{\\perp}$. Those of $x$-type form narrow bands of NEEs that conserve the integer-valued $x$-magnetization. Quantum evolution within a given band of each type is described by a Hamiltonian that belongs to either the ensemble of Preferred Basis Levi matrices ($z$-type) or Gaussian Orthogonal ensemble ($x$-type). We characterize the non-equilibrium dynamics using fractal dimension $D$ that depends on energy density (temperature) and plays a role of thermodynamic potential: $D=0$ in MBL phase, $0<D<1$ in NEE phase, $D\\rightarrow 1$ in ergodic phase in infinite temperature limit. MBL states coexist with NEEs in the same range of energies even at very large $B_{\\perp}$. Bands of NEE states can be used for new quantum search-like algorithms of population transfer in the low-energy part of spin-configuration space. Remarkably, the intermitted structure of the eigenspectrum emerges in quantum version of a statistically featureless Random Energy Model and is expected to exist in a class of paractically important NP-hard problems that unlike REM can be implemented on a computer with polynomial resources.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-02T19:56:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum spin glass",
      "dynamical phases",
      "featureless random energy model",
      "intermittency",
      "type form narrow bands"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}