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Register a new userConsistent partial bosonization of the extended Hubbard model
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We design an efficient and balanced approach that captures major effects of collective electronic fluctuations in strongly correlated fermionic systems using a simple diagrammatic expansion on a basis of dynamical mean-field theory. For this aim we perform a partial bosonization of collective fermionic fluctuations in leading channels of instability. We show that a simultaneous account for different bosonic channels can be done in a consistent way that allows to avoid the famous Fierz ambiguity problem. The present method significantly improves a description of an effective screened interaction $W$ in both, charge and spin channels, and has a great potential for application to realistic $GW$-like calculations for magnetic materials.
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The role of Klein factors is investigated for the bosonized Hamiltonian of the dimerized Hubbard model. Contrary to previous approaches we take into account their number changing property, i.e. we do not replace them by Majorana fermions. We show how to treat Klein factors in the framework of the self-consistent harmonic approximation, both for finite systems and in the thermodynamic limit.
We discuss the phase diagram of the extended Hubbard model with both attractive and repulsive local and nonlocal interactions. The extended dynamical mean-field theory (EDMFT) and the dual boson method (DB) are compared. The latter contains additional nonlocal correlation effects that are not incorporated in EDMFT. We find that EDMFT and DB give almost identical results in the attractive $V$ regime, where phase separation occurs. This is quite a difference with the previously studied repulsive $V$ regime, where EDMFT and DB give very different phase boundaries for the checkerboard order phase, especially at small $U$.
While the Hubbard model is the standard model to study Mott metal-insulator transitions, it is still unclear to which extent it can describe metal-insulator transitions in real solids, where non-local Coulomb interactions are always present. By using a variational principle, we clarify this issue for short- and long-ranged non-local Coulomb interactions for half-filled systems on bipartite lattices. We find that repulsive non-local interactions generally stabilize the Fermi-liquid regime. The metal-insulator phase boundary is shifted to larger interaction strengths to leading order linearly with non-local interactions. Importantly, non-local interactions can raise the order of the metal-insulator transition. We present a detailed analysis of how the dimension and geometry of the lattice as well as the temperature determine the critical non-local interaction leading to a first-order transition: for systems in more than two dimensions with non-zero density of states at the Fermi energy the critical non-local interaction is arbitrarily small; otherwise it is finite.
The self-consistent harmonic approximation is extended in order to account for the existence of Klein factors in bosonized Hamiltonians. This is important for the study of finite systems where Klein factors cannot be ignored a priori. As a test we apply the method to interacting spinless fermions with modulated hopping. We calculate the finite-size corrections to the energy gap and the Drude weight and compare our results with the exact solution for special values of the model parameters.
We extend previous real-space Hartree-Fock studies of static stripe stability to determine the phase diagram of the Hubbard model with anisotropic nearest-neighbor hopping t, by varying the on-site Coulomb repulsion U and investigating locally stable structures for representative hole doping levels x=1/8 and x=1/6. We also report the changes in stability of these stripes in the extended Hubbard model due to next-neighbor hopping t and to a nearest-neighbor Coulomb interaction V.
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