Effective Ising model for correlated systems with charge ordering

Abstract

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]

Dual boson approach with instantaneous interaction

“…In this work, we use the ladder equation to calcu-lateΠ 14,15,26,27 , which describes repeated particle-hole scattering mediated by the fermion-fermion vertex of the impurity model. The ladder DB approach with the frequency dependent bosonic hybridization shows a quantitatively good result for the susceptibility in agreement with Quantum Monte Carlo and Dynamical Cluster Approximation calculations in a broad range of Coulomb interactions and dopings [28][29][30] . The restriction to instantaneous interactions simply leads to the replacement of Λ ω by a constant Λ in Eq.…”

Spin dynamics of itinerant electrons: local magnetic moment formation and Berry phase

“…Static properties of effective bosonic models for spin or charge degrees of freedom, namely the exchange interaction between spin or charge densities, have been studied in previous works [39,40]. Description of the spin dynamics, which has not been performed in these works, is a non-trivial task that requires a careful separation of the precession of the vector spin field from the fluctuation of the absolute value of the local magnetic moment.…”

“…1 is introduced to simplify notations. The diagonal part of the kinetic interaction is given by the Heisenberg exchange interaction J ss i j for spin [39] and the Ising interaction J cc i j for charge [40] densities. The non-diagonal J ss i j (s s ) component gives rise to the antisymmetric anisotropic (Dzyaloshinskii-Moriya) and the symmetric anisotropic interactions (see, e.g., Ref.…”

“…In this paper, we solve this problem based on a modification and development [39][40][41][42] of the dual boson formalism [43][44][45][46][47]. Our aim is twofold: to derive properly the Berry phase term describing spin precession for fermionic (that is, itinerant) systems in terms of the physical bosonic variables, and to write a physical criterion for the formation of local magnetic moments.…”

Single boson exchange representation of the functional renormalization group for strongly interacting many-electron systems

“…In this perspective, the SBE decomposition offers a relatively simple way to circumvent this problem, expressing the DMFT vertex in terms of bosonic propagators and Yukawa couplings, which can then be used as initial conditions of a mixed boson-fermion flow. In this respect, it is worth stressing that the fermion-boson approach [59,60] has proven to be useful also in the context of diagrammatic extensions of DMFT [61] not based on the fRG formalisms.…”