2019/07/02 by Vadim N. Smelyanskiy, Vadim Smelyanskiy, Kostyantyn Kechedzhi +9 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Disordered Systems and Neural Networks (cond-mat.dis-nn) #Eigenvalues and eigenvectors #Ergodic theory #FOS: Physical sciences #Hamiltonian (control theory) #Mathematics #Neural Networks and Applications #Physics #Pure mathematics #Quantum #Quantum Physics (quant-ph) #Quantum dynamics #Quantum mechanics #Quantum number #Spin glass #Theoretical and Computational Physics #Type (biology) #cond-mat.dis-nn #quant-ph
paper · pdf · doi:10.48550/arxiv.1907.01609
16 pages, 12 figures
arxiv created 2019/07/02 · openalex publication_date 2019/07/02 · arxiv updated 2019/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \σz\ 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⊥. 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