Year: 2019
Type: article
Abstract: We study analytically and numerically the dynamics of the generalized Rosenzweig-Porter model, which is known to possess three distinct phases: ergodic, multifractal and localized phases. Our focus is on the survival probability \bm{R(t)} 𝐑 ( 𝐭 ) , the probability of finding the initial state after time \bm{t} 𝐭 . In particular, if the system is initially prepared in a highly-excited non-stationary state (wave packet) confined in space and containing a fixed fraction of all eigenstates, we show that \bm{R(t)} 𝐑 ( 𝐭 ) can be used as a dynamical indicator to distinguish these three phases. Three main aspects are identified in different phases. The ergodic phase is characterized by the standard power-law decay of \bm{R(t)} 𝐑 ( 𝐭 ) with periodic oscillations in time, surviving in the thermodynamic limit, with frequency equals to the energy bandwidth of the wave packet. In multifractal extended phase the survival probability shows an exponential decay but the decay rate vanishes in the thermodynamic limit in a non-trivial manner determined by the fractal dimension of wave functions. Localized phase is characterized by the saturation value of \bm{R(t\to\infty)=k} 𝐑 ( 𝐭 → ∞ ) = 𝐤 , finite in the thermodynamic limit \bm{N\rightarrow\infty} 𝐍 → ∞ , which approaches \bm{k=R(t\to 0)} 𝐤 = 𝐑 ( 𝐭 → 0 ) in this limit.
Source: SciPost Physics
Authors: Giuseppe De Tomasi, Mohsen Amini, Soumya Bera, Ivan Khaymovich, Vladimir Kravtsov
Institutions: Max Planck Institute for the Physics of Complex Systems, Technical University of Munich, University of Isfahan, Indian Institute of Technology Bombay, The Abdus Salam International Centre for Theoretical Physics (ICTP), University of California, Santa Barbara, Landau Institute for Theoretical Physics
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Funders: National Science Foundation, Department of Science and Technology, Ministry of Science and Technology, India, Deutsche Forschungsgemeinschaft, Russian Foundation for Basic Research, University of California, Santa Barbara, Kavli Institute for Theoretical Physics, University of California, Santa Barbara
OpenAlex ID: W2804668329