Anomalous multifractality in quantum chains with strongly correlated disorder

Abstract

We demonstrate numerically that a robust and unusual multifractal regime can emerge in a one-dimensional quantum chain with maximally correlated disorder, above a threshold disorder strength. This regime is preceded by a mixed and an extended regime at weaker disorder strengths, with the former hosting both extended and multifractal eigenstates. The multifractal states we find are markedly different from conventional multifractal states in their structure, as they reside approximately uniformly over a continuous segment of the chain, and the lengths of these segments scale non-trivially with system size. This anomalous nature also leaves imprints on dynamics. An initially localised wavepacket shows ballistic transport, in contrast to the slow, generally sub-diffusive, transport commonly associated with multifractality. However, the timescale over which this ballistic transport persists again scales non-trivially with the system size.

arXiv comment6 pages, 6 figures + supplementary material (2 pages); minor modifications and updated references

References in corpus (32)

• Anderson Transitions
• Scaling Theory of the Integer Quantum Hall Effect
• Localization and Mobility Edge in One-Dimensional Potentials with Correlated Disorder
• Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
• Multifractal Scalings across the Many-Body Localization Transition
• Ergodicity breaking in a model showing many-body localization
• Fluctuations of the inverse participation ratio at the Anderson transition
• Multifractality and critical fluctuations at the Anderson transition
• One-dimensional quasicrystals with power-law hopping
• A random matrix model with localization and ergodic transitions
• Mutifractal Analysis of Broadly Distributed Observables at Criticality
• Rare thermal bubbles at the many-body localization transition from the Fock space point of view
• Spectral Rigidity and Eigenfunction Correlations at the Anderson Transition
• Multifractality of wavefunctions at the quantum Hall transition revisited
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• Sub-diffusion in the Anderson model on random regular graph
• Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
• Fock-space correlations and the origins of many-body localisation
• The Lévy-Rosenzweig-Porter random matrix ensemble
• Fluctuations of the correlation dimension at metal-insulator transitions
• Multifractality of eigenstates in the delocalized non-ergodic phase of some random matrix models : Wigner-Weisskopf approach
• Critical statistics in a power-law random banded matrix ensemble
• Multifractality without fine-tuning in a Floquet quasiperiodic chain
• Mobility edge and multifractality in a periodically driven Aubry-André model
• Fock-space anatomy of eigenstates across the many-body localisation transition
• Anderson Localization in 1D Systems with Correlated Disorder
• Localisation on certain graphs with strongly correlated disorder
• Anomalously large critical regions in power-law random matrix ensembles
• Multifractality of Hamiltonians with power-law transfer terms
• Anderson localization transition with long-ranged hoppings : analysis of the strong multifractality regime in terms of weighted Levy sums
• Multifractality in the generalized Aubry-Andre quasiperiodic localization model with power-law hoppings or power-law Fourier coefficients
• Generalized Dyson model: nature of zero mode and its implication in dynamics

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• A Lévy flight for electrons in graphene: superdiffusive-to-diffusive transport transition
• Unconventional edge states in a two-leg ladder
• Periodically and aperiodically Thue-Morse driven long-range systems: from dynamical localization to slow dynamics
• Critical dynamics of long-range quantum disordered systems
• Multifractality in monitored single-particle dynamics
• Bound states in one-dimensional systems with colored noise
• Multifractality in high-dimensional graphs induced by correlated radial disorder
• Krylov-space anatomy and spread complexity of a disordered quantum spin chain
• The Wishart--Rosenzweig--Porter random matrix ensemble
• Two-strand ladder network variants: localization, multifractality, and quantum dynamics under an Aubry-André-Harper kind of quasiperiodicity
• Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree
• Disorder averaging in random lattice models with periodic boundary conditions: Application to models with uncorrelated and correlated disorder
• Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder
• Replica approach to the generalized Rosenzweig-Porter model
• Non-self-averaging topological Anderson insulator