Critical dynamics of long-range quantum disordered systems

• URL: http://arxiv.org/abs/2307.00999v1
• Date: Mon, 3 Jul 2023 13:25:54 GMT
• Title: Critical dynamics of long-range quantum disordered systems
• Authors: Weitao Chen, Gabriel Lemarie, Jiangbin Gong
• Abstract summary: 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.
• Score: 0.3007949058551534
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Long-range hoppings in quantum disordered systems are known to yield quantum multifractality, whose features can go beyond the characteristic properties associated with an Anderson transition. Indeed, critical dynamics of long-range quantum systems can exhibit anomalous dynamical behaviours distinct from those at the Anderson transition in finite dimensions. In this paper, we propose a phenomenological model of wave packet expansion in long-range hopping systems. We consider both their multifractal properties and the algebraic fat tails induced by the long-range hoppings. Using this model, we analytically derive the dynamics of moments and Inverse Participation Ratios of the time-evolving wave packets, in connection with the multifractal dimension of the system. To validate our predictions, we perform numerical simulations of a Floquet model that is analogous to the power law random banded matrix ensemble. Unlike the Anderson transition in finite dimensions, the dynamics of such systems cannot be adequately described by a single parameter scaling law that solely depends on time. Instead, it becomes crucial to establish scaling laws involving both the finite-size and the time. Explicit scaling laws for the observables under consideration are presented. Our findings are of considerable interest towards applications in the fields of many-body localization and Anderson localization on random graphs, where long-range effects arise due to the inherent topology of the Hilbert space.

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