Quantum logarithmic multifractality

• URL: http://arxiv.org/abs/2312.17481v1
• Date: Fri, 29 Dec 2023 05:56:52 GMT
• Title: Quantum logarithmic multifractality
• Authors: Weitao Chen, Olivier Giraud, Jiangbin Gong, Gabriel Lemari\'e
• Abstract summary: This work reports an exotic multifractal behavior, dubbed "logarithmic multifractality", in effectively infinite-dimensional systems undergoing the Anderson transition. Our findings offer crucial insights into strong finite-size effects and slow dynamics in complex systems undergoing the Anderson transition.
• Score: 0.6963971634605796
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Through a combination of rigorous analytical derivations and extensive numerical simulations, this work reports an exotic multifractal behavior, dubbed "logarithmic multifractality", in effectively infinite-dimensional systems undergoing the Anderson transition. In marked contrast to conventional multifractal critical properties observed at finite-dimensional Anderson transitions or scale-invariant second-order phase transitions, in the presence of logarithmic multifractality, eigenstate statistics, spatial correlations, and wave packet dynamics can all exhibit scaling laws which are algebraic in the logarithm of system size or time. Our findings offer crucial insights into strong finite-size effects and slow dynamics in complex systems undergoing the Anderson transition, such as the many-body localization transition.

Related papers

• Ab-Initio Approach to Many-Body Quantum Spin Dynamics [0.0]
  We employ the multilayer multiconfiguration time-dependent Hartree framework to simulate the many-body spin dynamics of the Heisenberg model. We show that ML-MCTDH accurately captures the time evolution of one- and two-body observables in both one- and two-dimensional lattices. Our results indicate that the multilayer structure of ML-MCTDH is a promising numerical framework for handling the dynamics of generic many-body spin systems.
  arXiv  Detail & Related papers  (2024-11-20T10:42:35Z)
• Entanglement and operator correlation signatures of many-body quantum Zeno phases in inefficiently monitored noisy systems [49.1574468325115]
  The interplay between information-scrambling Hamiltonians and local continuous measurements hosts platforms for exotic measurement-induced phase transition. We identify a non-monotonic dependence on the local noise strength in both the averaged entanglement and operator correlations. The analysis of scaling with the system size in a finite length chain indicates that, at finite efficiency, this effect leads to distinct MiPTs for operator correlations and entanglement.
  arXiv  Detail & Related papers  (2024-07-16T13:42:38Z)
• Describing the critical behavior of the Anderson transition in infinite dimension by random-matrix ensembles: logarithmic multifractality and critical localization [0.6374763930914524]
  This paper investigates two random matrix ensembles tailored to capture the critical behavior of the Anderson transition in infinite dimension. Our study unveils two types of critical behaviors: logarithmic multifractality and critical localization. Our findings enable broad applicability to systems with pronounced finite-size effects and slow dynamics.
  arXiv  Detail & Related papers  (2024-05-12T12:55:28Z)
• Attractor Memory for Long-Term Time Series Forecasting: A Chaos Perspective [63.60312929416228]
  textbftextitAttraos incorporates chaos theory into long-term time series forecasting. We show that Attraos outperforms various LTSF methods on mainstream datasets and chaotic datasets with only one-twelfth of the parameters compared to PatchTST.
  arXiv  Detail & Related papers  (2024-02-18T05:35:01Z)
• Quantum multifractality as a probe of phase space in the Dicke model [0.0]
  We study the multifractal behavior of coherent states projected in the energy eigenbasis of the spin-boson Dicke Hamiltonian. By examining the linear approximation and parabolic correction to the mass exponents, we find ergodic and multifractal coherent states.
  arXiv  Detail & Related papers  (2023-07-07T19:04:26Z)
• Critical dynamics of long-range quantum disordered systems [0.3007949058551534]
  Long-range hopping in quantum disordered systems can yield quantum multifractality. We propose a model of wave packet expansion in long-range hopping systems. Our findings are of considerable interest towards applications in the fields of many-body localization and Anderson localization on random graphs.
  arXiv  Detail & Related papers  (2023-07-03T13:25:54Z)
• Onset of scrambling as a dynamical transition in tunable-range quantum circuits [0.0]
  We identify a dynamical transition marking the onset of scrambling in quantum circuits with different levels of long-range connectivity. We show that as a function of the interaction range for circuits of different structures, the tripartite mutual information exhibits a scaling collapse. In addition to systems with conventional power-law interactions, we identify the same phenomenon in deterministic, sparse circuits.
  arXiv  Detail & Related papers  (2023-04-19T17:37:10Z)
• Order-invariant two-photon quantum correlations in PT-symmetric interferometers [62.997667081978825]
  Multiphoton correlations in linear photonic quantum networks are governed by matrix permanents. We show that the overall multiphoton behavior of a network from its individual building blocks typically defies intuition. Our results underline new ways in which quantum correlations may be preserved in counterintuitive ways even in small-scale non-Hermitian networks.
  arXiv  Detail & Related papers  (2023-02-23T09:43:49Z)
• Genuine Multipartite Correlations in a Boundary Time Crystal [56.967919268256786]
  We study genuine multipartite correlations (GMC's) in a boundary time crystal (BTC) We analyze both (i) the structure (orders) of GMC's among the subsystems, as well as (ii) their build-up dynamics for an initially uncorrelated state.
  arXiv  Detail & Related papers  (2021-12-21T20:25:02Z)
• Continuous and time-discrete non-Markovian system-reservoir interactions: Dissipative coherent quantum feedback in Liouville space [62.997667081978825]
  We investigate a quantum system simultaneously exposed to two structured reservoirs. We employ a numerically exact quasi-2D tensor network combining both diagonal and off-diagonal system-reservoir interactions with a twofold memory for continuous and discrete retardation effects. As a possible example, we study the non-Markovian interplay between discrete photonic feedback and structured acoustic phononovian modes, resulting in emerging inter-reservoir correlations and long-living population trapping within an initially-excited two-level system.
  arXiv  Detail & Related papers  (2020-11-10T12:38:35Z)
• The role of boundary conditions in quantum computations of scattering observables [58.720142291102135]
  Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. As with present-day calculations, quantum computation strategies still require the restriction to a finite system size. We quantify the volume effects for various $1+1$D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty.
  arXiv  Detail & Related papers  (2020-07-01T17:43:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.