Superdiffusion in a random two-dimensional system with time-reversal symmetry and long-range hopping
Abstract
Although it is recognized that Anderson localization takes place for all states at a dimension d less or equal 2, while delocalization is expected for hopping V(r) decreasing with the distance slower or as r-d, the localization problem in the crossover regime for the dimension d = 2 and hopping V(r) ∝ r⁻² is not resolved yet. Following earlier suggestions we show that for the hopping determined by two-dimensional anisotropic dipole-dipole interactions in the presence of time-reversal symmetry there exist two distinguishable phases at weak and strong disorder. The first phase is characterized by ergodic dynamics and superdiffusive transport, while the second phase is characterized by diffusive transport and delocalized eigenstates with fractal dimension less than 2. The transition between phases is resolved analytically using the extension of scaling theory of localization and verified numerically using an exact numerical diagonalization.
Related
- Quantum metrology of hopping strength in one-dimensional chains
- Entanglement transitions and multifractality in monitored free-fermions with random long-range hopping
- Time-reversal symmetry breaking and inherent Josephson diodes in a multi-component order parameter superconductor
- Type-II quantum spin Hall insulator without time-reversal symmetry
- Fractionalization-Induced Time-Reversal Symmetry Breaking at Continuous Superconducting Transitions in Low-Symmetry Kondo Lattices
BibTeX
@article{deng2026superdiffusion,
title = {{Superdiffusion in a random two-dimensional system with time-reversal symmetry and long-range hopping}},
author = {Xiaolong Deng and Ivan M Khaymovich and Alexander Burin},
journal = {Physical Review B},
year = {2026},
month = sep,
doi = {10.1103/physrevb.109.174208},
url = {https://hal.science/hal-05765835v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Superdiffusion in a random two-dimensional system with time-reversal symmetry and long-range hopping
AU - Xiaolong Deng
AU - Ivan M Khaymovich
AU - Alexander Burin
PY - 2026
DA - 2026/09/29
JO - Physical Review B
DO - 10.1103/physrevb.109.174208
UR - https://hal.science/hal-05765835v1
AB - Although it is recognized that Anderson localization takes place for all states at a dimension d less or equal 2, while delocalization is expected for hopping V(r) decreasing with the distance slower or as r-d, the localization problem in the crossover regime for the dimension d = 2 and hopping V(r) ∝ r⁻² is not resolved yet. Following earlier suggestions we show that for the hopping determined by two-dimensional anisotropic dipole-dipole interactions in the presence of time-reversal symmetry there exist two distinguishable phases at weak and strong disorder. The first phase is characterized by ergodic dynamics and superdiffusive transport, while the second phase is characterized by diffusive transport and delocalized eigenstates with fractal dimension less than 2. The transition between phases is resolved analytically using the extension of scaling theory of localization and verified numerically using an exact numerical diagonalization.
SN - 2469-9950
SN - 2469-9969
ER -