Abstract:We develop a real space cluster extension of the typical medium theory (cluster-TMT) to study Anderson localization. By construction, the cluster-TMT approach is formally equivalent to the real space cluster extension of the dynamical mean field theory. Applying the developed method to the 3D Anderson model with a box disorder distribution, we demonstrate that cluster-TMT successfully captures the localization phenomena in all disorder regimes. As a function of the cluster size, our method obtains the correct critical disorder strength for the Anderson localization in 3D, and systematically recovers the re-entrance behavior of the mobility edge. From a general perspective, our developed methodology offers the potential to study Anderson localization at surfaces within quantum embedding theory. This opens the door to studying the interplay between topology and Anderson localization from first principles.Keywords: metal insulator transition; Anderson localization; random disorder; typical medium theory; dynamical mean field theory; coherent potential approximation; dynamical cluster approximation; cellular dynamical mean field theory; cluster mean field theory
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In summary, we successfully observed the local magnon mode change on FeTiO3 in real space by the dynamic magnetic pair-density function (DymPDF) analysis. This real space image provides a novel possibility to study local spin dynamics in addition to the nearly static magnetic pair-density of various magnetic systems at low energy. The latter is particularly important because nuclear scattering components can be naturally removed by limiting Q-range. It means that a tedious process to subtract nuclear Bragg peaks from the measured pattern can be avoided. Possible suitable research by DymPDF would be molecular cluster magnets, nanomagnets, local magnetic clusters, and magnetic short-range orders in addition to magnetic amorphous alloys and magnetic quasicrystals. The local magnetic clusters are known to appear in spin frustration systems as a spin molecule in MgCr2O415. In a superconducting state, spin resonance mode appears in an unconventional superconductor such as CeCoIn516. By DymPDF analysis, it becomes possible to check whether spin-singlet or spin-triplet state is realized in the superconducting state, in addition to the correlation length that can be compared with the superconducting coherence length. Magnetic percolation network such as fracton17 or Mott transition by anion exchange18 may also be a suitable system to study a decay of the magnetic pair-density as a function of a bond length in the network. DymPDF analysis can also be used to study the spin dynamics of a crystalline magnet that can be synthesized only in powder form. The application is not limited to these systems. There can be vast other applications by the DymPDF analysis. 2ff7e9595c
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