Localization and critical diffusion of quantum dipoles in two dimensions

Abstract

We discuss quantum propagation of dipole excitations in two dimensions. This problem differs from the conventional Anderson localization due to existence of long range hops. We found that the critical wavefunctions of the dipoles always exist which manifest themselves by a scale independent diffusion constant. If the system is T-invariant the states are critical for all values of the parameters. Otherwise, there can be a "metal-insulator" transition between this "ordinary" diffusion and the Levy-flights (the diffusion constant logarithmically increasing with the scale). These results follow from the two-loop analysis of the modified non-linear supermatrix $\sigma$-model.

4.2 pages

References in corpus (1)

• Effect of Long Range Disorder on Electron Motion in Two Dimensions

Cited by in corpus (17)

• Duality in power-law localization in disordered one-dimensional systems
• Dynamics and Transport at the Threshold of Many-Body Localization
• Quantum Levy flights and multifractality of dipolar excitations in a random system
• Emergent locality in systems with power-law interactions
• Levy flights and multifractality in quantum critical diffusion and in classical random walks on fractals
• Spin transport in long-range interacting one-dimensional chain
• Suppression of heating by long-range interactions in periodically driven spin chains
• Quantum simulations of localization effects with dipolar interactions
• Nonequilibrium phase transition in an open quantum spin system with long-range interaction
• Anisotropy-mediated reentrant localization
• Spin transport in disordered long-range interacting spin chain
• Electromagnetic field assisted exciton diffusion in moiré superlattices
• Duality between disordered nodal semimetals and systems with power-law hopping
• Single-particle localization in a two-dimensional Rydberg spin system
• Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping
• Energy-level statistics in strongly disordered systems with power-law hopping
• Dynamical control in a prethermalized molecular ultracold plasma: Local dissipation drives global relaxation