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.

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

References in corpus (11)

• Anderson Transitions
• Ergodicity breaking in a model showing many-body localization
• Rare thermal bubbles at the many-body localization transition from the Fock space point of view
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
• The Lévy-Rosenzweig-Porter random matrix ensemble
• Mobility edge and multifractality in a periodically driven Aubry-André model
• Fock-space anatomy of eigenstates across the many-body localisation transition
• Localisation on certain graphs with strongly correlated disorder
• 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

Cited by in corpus (19)

• Critical-to-Insulator Transitions and Fractality Edges in Perturbed Flatbands
• Flat-band-based multifractality in the all-band-flat diamond chain
• Delayed Thermalization in Mass-Deformed SYK
• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
• 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