Related papers: Anderson localization: A view from Krylov space
Mixed-effects models are widely used to model data with hierarchical grouping structures and high-cardinality categorical predictor variables. However, for high-dimensional crossed random effects, current standard computations relying on…
Recently, a novel measure for the complexity of operator growth is proposed based on Lanczos algorithm and Krylov recursion method. We study this Krylov complexity in quantum mechanical systems derived from some well-known local toric…
We provide convergence rates for Krylov subspace solutions to the trust-region and cubic-regularized (nonconvex) quadratic problems. Such solutions may be efficiently computed by the Lanczos method and have long been used in practice. We…
The spectral approach to infinite disordered crystals is applied to an Anderson-type Hamiltonian to demonstrate the existence of extended states for nonzero disorder in 2D lattices of different geometries. The numerical simulations shown…
We investigate various aspects of the Lanczos coefficients in a family of free Lifshitz scalar theories, characterized by their integer dynamical exponent, at finite temperature. In this non-relativistic setup, we examine the effects of…
As part of condensed-matter physics, the field of Anderson localization concerns the study of conductance of electrons in a random medium. We summarize and explain the results obtained in "A new numerical approach to Anderson…
We examine the localization properties of the Anderson Hamiltonian with additional off-diagonal disorder using the transfer-matrix method and finite-size scaling. We compute the localization lengths and study the metal-insulator transition…
The localization behavior of the one-dimensional Anderson model with correlated and uncorrelated purely off-diagonal disorder is studied. Using the transfer matrix method, we derive an analytical expression for the localization length at…
Anderson localization problem for non-interacting two-dimensional electron gas subject to strong magnetic field, disordered potential and spin-orbit coupling is studied numerically on a square lattice. The nature of the corresponding…
We study Anderson localization in a discrete-time quantum map dynamics in one dimension with nearest-neighbor hopping strength $\theta$ and quasienergies located on the unit circle. We demonstrate that strong disorder in a local phase field…
The growth of simple operators is essential for the emergence of chaotic dynamics and quantum thermalization. Recent studies have proposed different measures, including the out-of-time-order correlator and Krylov complexity. It is…
We calculate the effective spatial dimension $d_\text{IR}$ of electron modes at critical points of 3D Anderson models in various universality classes (O,U,S,AIII). The results are equal within errors, and suggest the super-universal value…
We study the Loschmidt echo and the dynamical free energy of the Anderson model after a quench of the disorder strength. If the initial state is extended and the eigenstates of the post-quench Hamiltonian are strongly localized, we argue…
We study numerically the critical behavior at the localization transition in the Anderson model on infinite Bethe lattice and on random regular graphs. The focus is on the case of coordination number $m+1 = 3$, with a box distribution of…
Many-body localization is characterized by a slow logarithmic growth of the entanglement entropy after a global quantum quench while the local memory of an initial density imbalance remains at infinite time. We investigate how much the…
We study the quantum localization phenomena of noninteracting particles in one-dimensional lattices based on tight-binding models with various forms of hopping terms beyond the nearest neighbor, which are generalizations of the famous…
We provide a complete and self-contained proof of spectral and dynamical localization for the one-dimensional Anderson model, starting from the positivity of the Lyapunov exponent provided by F\"urstenberg's theorem. That is, a…
We prove that a strongly disordered two-dimensional system localizes with a localization length given analytically. We get a scaling law with a critical exponent is $\nu=1$ in agreement with the Chayes criterion $\nu\ge 1$. The case we are…
For large scale electronic structure calculation, the Krylov subspace method is introduced to calculate the one-body density matrix instead of the eigenstates of given Hamiltonian. This method provides an efficient way to extract the…
The localization behavior of the Anderson model with anisotropic hopping integral t for weakly coupled planes and weakly coupled chains is investigated both numerically with the transfer matrix method and analytically within the…