Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userInvestigation of the effective interactions for the Emery model by the constrained random-phase approximation and constrained functional renormalization group
91
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The effective interaction of downfolded low-energy models for electrons in solids can be obtained by integrating out the high energy bands away from the target band near the Fermi level. Here, we apply the constrained random-phase approximation (cRPA) and constrained functional renormalization group (cfRG), which can go beyond cRPA by including all one-loop diagrams, to calculate and compare the effective interactions of the three-band Emery model, which is often used to investigate cuprate high-temperature superconductors. At half band filling, we find that the effective interaction increases as the charge transfer energy ($Delta_{dp}$) increases and similar behavior is obtained as a function of the interatomic 2$p$-3$d$ interaction ($U_{dp}$). However, the effective interaction is more sensitive to $Delta_{dp}$ than $ U_{dp}$. For most of the parameter sets, the effective static interaction is overscreened in cRPA compared to cfRG. The low-energy models at half-filling are solved within dynamical mean-field theory (DMFT). The results show that despite the different static interactions, the systems with cRPA and cfRG interaction exhibit a Mott transition at similar values of $Delta_{dp}$. We also investigate the effective interaction as a function of doping. The cfRG effective interaction decreases as the electron number increases and displays a trend opposite to that of cRPA. Antiscreening is observed for the hole-doped case. For all the cases studied, the near-cancellation of the direct particle-hole channel is observed. This indicates that at least for the downfolding of the onsite interaction terms, methods beyond cRPA may be required.
rate research
Read More
The many-body theory of interacting electrons poses an intrinsically difficult problem that requires simplifying assumptions. For the determination of electronic screening properties of the Coulomb interaction, the Random Phase Approximation (RPA) provides such a simplification. Here, we explicitly show that this approximation is justified for band structures with sizeable band gaps. This is when the electronic states responsible for the screening are energetically far away from the Fermi level, which is equivalent to a short electronic propagation length of these states. The RPA contains exactly those diagrams in which the classical Coulomb interaction covers all distances, whereas neglected vertex corrections involve quantum tunneling through the barrier formed by the band gap. Our analysis of electron-electron interactions provides a real-space analogy to Migdals theorem on the smallness of vertex corrections in electron-phonon problems. An important application is the increasing use of constrained Random Phase Approximation (cRPA) calculations of effective interactions. We find that their usage of Kohn-Sham energies already accounts for the leading local (excitonic) vertex correction in insulators.
Recent experiments on twisted bilayer graphene show the urgent need for establishing a low-energy lattice model for the system. We use the constrained random phase approximation to study the interaction parameters of such models taking into account screening from the moire bands left outside the model space. Based on an atomic-scale tight-binding model, we develop a numerically tractable approximation to the polarization function and study its behavior for different twist angles. We find that the polarization has three different momentum regimes. For small momenta, the polarization is quadratic, leading to a linear dielectric function expected for a two-dimensional dielectric material. For large momenta, the polarization becomes independent of the twist angle and approaches that of uncoupled graphene layers. In the intermediate momentum regime, the dependence on the twist-angle is strong. Close to the largest magic angle the dielectric function peaks at a momentum of $~1/(4 : nm)$ attaining values of 25, meaning very strong screening at intermediate distances. We also calculate the effective screened Coulomb interaction in real space and give estimates for the on-site and extended interaction terms for the recently developed hexagonal-lattice model. For free-standing TBG the effective interaction decays slower than $1/r$ at intermediate distances $r$, while it remains essentially unscreened at large enough $r$.
We have developed a fully consistent framework for calculations in the Quasiparticle Random Phase Approximation (QRPA) with $NN$ interactions from the Similarity Renormalization Group (SRG) and other unitary transformations of realistic interactions. The consistency of our calculations, which use the same Hamiltonian to determine the Hartree-Fock-Bogoliubov (HFB) ground states and the residual interaction for QRPA, guarantees an excellent decoupling of spurious strength, without the need for empirical corrections. While work is under way to include SRG-evolved 3N interactions, we presently account for some 3N effects by means of a linearly density-dependent interaction, whose strength is adjusted to reproduce the charge radii of closed-shell nuclei across the whole nuclear chart. As a first application, we perform a survey of the monopole, dipole, and quadrupole response of the calcium isotopic chain and of the underlying single-particle spectra, focusing on how their properties depend on the SRG parameter $lambda$. Unrealistic spin-orbit splittings suggest that spin-orbit terms from the 3N interaction are called for. Nevertheless, our general findings are comparable to results from phenomenological QRPA calculations using Skyrme or Gogny energy density functionals. Potentially interesting phenomena related to low-lying strength warrant more systematic investigations in the future.
We present a general frame to extend functional renormalization group (fRG) based computational schemes by using an exactly solvable interacting reference problem as starting point for the RG flow. The systematic expansion around this solution accounts for a non-perturbative inclusion of correlations. Introducing auxiliary fermionic fields by means of a Hubbard-Stratonovich transformation, we derive the flow equations for the auxiliary fields and determine the relation to the conventional weak-coupling truncation of the hierarchy of flow equations. As a specific example we consider the dynamical mean-field theory (DMFT) solution as reference system, and discuss the relation to the recently introduced DMF$^2$RG and the dual-fermion formalism.
We present a functional renormalization group analysis of superconductivity in the ground state of the attractive Hubbard model on a square lattice. Spontaneous symmetry breaking is treated in a purely fermionic setting via anomalous propagators and anomalous effective interactions. In addition to the anomalous interactions arising already in the reduced BCS model, effective interactions with three incoming legs and one outgoing leg (and vice versa) occur. We accomplish their integration into the usual diagrammatic formalism by introducing a Nambu matrix for the effective interactions. From a random-phase approximation generalized through use of this matrix we conclude that the impact of the 3+1 effective interactions is limited, especially considering the effective interactions important for the determination of the order parameter. The exact hierarchy of flow equations for one-particle irreducible vertex functions is truncated on the two-particle level, with higher-order self-energy corrections included in a scheme proposed by Katanin. Using a parametrization of effective interactions by patches in momentum space, the flow equations can be integrated numerically to the lowest scales without encountering divergences. Momentum-shell as well as interaction-flow cutoff functions are used, including a small external field or a large external field and a counterterm, respectively. Both approaches produce momentum-resolved order parameter values directly from the microscopic model. The size of the superconducting gap is in reasonable agreement with expectations from other studies.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
