Strong Correlation Effects and Localization in Metallic Systems (Bulletin of Pure and Applied Sciences – Physics, 2022)
We have studied strong correlation effects and localization in metallic systems. Strong  correlation effects and localization occurred in metallic systems due to strong electron-electron  interactions and strong electron phonon coupling. Strong electron-phonon interactions have  been found in such materials as cuprates, fullerides and manganites. The interplay of electron electron and electron-phonon interactions in these correlated systems leaded to coexistence of  or competition between various phases such as super conductivity, charge-density-wave or  spin–density wave phases or formation of novel non Fermi liquid phases, polarons,  bipolarons and so on. We have considered Holstein-Hubbard model for our work. The  Holstein-Hubbard model provides on over simplified description of both electron-electron  and electron-phonon interactions, it retains to be the relevant ingredients of a system in which  electrons experience simultaneously an instantaneous short range repulsion and a phonon mediated retarded attraction. In spite of its formal simplicity, it is not exactly solvable even in  one dimension. So quantum simulators of Fermi-Hubbard modes based on either fermionic  atoms inoptical lattice or electrons in artificial quantum dot crystals have been used. In our  work a classical analog simulator was theoretically proposed for the two site Holstein Hubbard model based on light transport in engineered waveguide lattices, which is capable of  reproducing the temporal dynamics of the quantum model in Fock space as spatial evolution  in photonic lattice. We have found that in the strong correlation regime the periodic temporal  dynamics exhibited by the Holstein-Hubbard Hamiltonian, related to the excitation Holstein  polarons has been explained in terms of generalized Bloch oscillations of a single particle in a  semi-infinite inhomogeneous tight binding lattice. Light transport in two dimensional  photonic lattices simulated in Fock space the hopping dynamics of two correlated electrons on  a one dimensional lattice and exploited to visualize such phenomena as correlated tunneling  of bond electron-electron molecules and their coherent motion under the action of d.c. or a.c.  fields. The obtained results were found in good agreement with previous results.