AI Article Synopsis
- The study investigates how dipole excitations propagate in two-dimensional systems, highlighting the differences from traditional Anderson localization due to long-range hopping effects.
- It finds that critical wave functions for dipoles consistently exist, indicated by a diffusion constant that doesn't change with scale.
- If the system is time-invariant, critical states occur across all parameter values; otherwise, a "metal-insulator" transition can occur, transitioning from regular diffusion to Levy flights, where the diffusion constant grows logarithmically with the scale.
Article Abstract
We discuss quantum propagation of dipole excitations in two dimensions. This problem differs from the conventional Anderson localization due to the existence of long-range hops. We find that the critical wave functions 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 nonlinear supermatrix σ model.
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| http://dx.doi.org/10.1103/PhysRevLett.107.076401 | DOI Listing |
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