Extended dynamical mean-field theory (EDMFT) is insufficient to describe non-local effects in strongly correlated systems, since corrections to the mean-field solution are generally large. We present an efficient scheme for the construction of diagrammatic extensions of EDMFT that avoids usual double counting problem by using an exact change of variables (the Dual Boson formalism) to distinguish the correlations included in the dynamical mean-field solution and those beyond. With a computational efficiency comparable to EDMFT+GW approach, our scheme significantly improves on the charge order transition phase boundary in the extended Hubbard model.

Valley polarization in graphene breaks inversion symmetry and therefore leads to second-harmonic generation. We present a complete theory of this effect within a single-particle approximation. It is shown that this may be a sensitive tool to measure the valley polarization created, e.g., by polarized light and, thus, can be used for a development of ultrafast valleytronics in graphene.

Collective electronic fluctuations in correlated materials give rise to various important phenomena, such as charge ordering, superconductivity, Mott insulating and magnetic phases, and plasmon and magnon modes. Unfortunately, the description of these correlation effects requires significant effort, since they almost entirely rely on strong local and nonlocal electron-electron interactions. Some collective phenomena, such as magnetism, can be sufficiently described by simple Heisenberg-like models that are formulated in terms of bosonic variables. This fact suggests that other many-body excitations can also be described by simple bosonic models in the spirit of Heisenberg theory. Here we derive an effective bosonic action for charge degrees of freedom for the extended Hubbard model and define a physical regime where the obtained action reduces to a classical Hamiltonian of an effective Ising model. arXiv:1806.04927v3 [cond-mat.str-el]

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