Effective Low-energy Interaction Research Articles

Efficient vertex parametrization for the constrained functional renormalization group for effective low-energy interactions in multiband systems

We describe an efficient approximation for the electron-electron interaction in the determination of the low-energy effective interaction in multiband lattice systems. By using ideas for channel decomposition, form-factor expansion and the truncated-unity technique we describe the interaction as arising from the non-local and orbital-dependent coupling of particle-hole and particle-particle bilinears formed by fields residing in the same one or two orbitals. This allows us to employ the constrained functional renormalization group (cfRG) with a suitable momentum and frequency discretization. The approach gives insights into the non-local screening of spin and charge interactions when bands away from the Fermi level are integrated out. Specifically, we compute the effective low-energy interactions in the low-energy target band of a three-band model with onsite and non-local bare interactions. We show that the cfRG adds important features to the effective target-band interaction that cannot be found using the constrained random phase approximation (cRPA).

P -wave superconductivity in weakly repulsive 2D Hubbard model with Zeeman splitting and weak Rashba spin-orbit coupling

We study the superconducting order in a two-dimensional square lattice Hubbard model with weak repulsive interactions, subject to a Zeeman field and weak Rashba spin-orbit interactions. Diagonalizing the non-interacting Hamiltonian leads to two separate bands, and by deriving an effective low-energy interaction we find the mean field gap equations for the superconducting order parameter on the bands. Solving the gap equations just below the critical temperature, we find that superconductivity is caused by Kohn-Luttinger type interaction, while the pairing symmetry of the bands are indirectly affected by the spin-orbit coupling. The dominating attractive momentum channel of the Kohn-Luttinger term depends on the filling fraction $n$ of the system, and it is therefore possible to change the momentum dependence of the order parameter by tuning $n$. Moreover, $n$ also determines which band has the highest critical temperature. Rotating the magnetic field changes the momentum dependence from states that for small momenta reduce to a chiral $p_x \pm i p_y$ type state for out-of-plane fields, to a nodal p-wave type state for purely in-plane fields.

Renormalization of effective interactions in a negative charge transfer insulator

We compute from first principles the effective interaction parameters appropriate for a low-energy description of the rare-earth nickelate LuNiO$_{3}$ involving the partially occupied $e_g$ states only. The calculation uses the constrained random-phase approximation and reveals that the effective on-site Coulomb repulsion is strongly reduced by screening effects involving the oxygen-$p$ and nickel-$t_{2g}$ states. The long-range component of the effective low-energy interaction is also found to be sizeable. As a result, the effective on-site interaction between parallel-spin electrons is reduced down to a small negative value. This validates effective low-energy theories of these materials proposed earlier. Electronic structure methods combined with dynamical mean-field theory are used to construct and solve an appropriate low-energy model and explore its phase diagram as a function of the on-site repulsion and Hund's coupling. For the calculated values of these effective interactions we find, in agreement with experiments, that LuNiO$_{3}$ is a metal without disproportionation of the $e_g$ occupancy when considered in its orthorhombic structure, while the monoclinic phase is a disproportionated insulator.

Singlet model interference effects with high scale UV physics

One of the simplest extensions of the Standard Model (SM) is the addition of a scalar gauge singlet, S. If S is not forbidden by a symmetry from mixing with the Standard Model Higgs boson, the mixing will generate non-SM rates for Higgs production and decays. In general, there could also be unknown high energy physics that generates additional effective low energy interactions. We show that interference effects between the scalar resonance of the singlet model and the effective field theory (EFT) operators can have significant effects in the Higgs sector. We examine a non-$Z_2$ symmetric scalar singlet model and demonstrate that a fit to the 125 GeV Higgs boson couplings and to limits on high mass resonances, S, exhibit an interesting structure and possible large cancellations of effects between the resonance contribution and the new EFT interactions, that invalidate conclusions based on the renormalizable singlet model alone.

Effective three-particle interactions in low-energy models for multiband systems

We discuss different approximations for effective low-energy interactions in multi-band models for weakly correlated electrons. In the study of Fermi surface instabilities of the conduction band(s), the standard approximation consists only keeping those terms in the bare interactions that couple only to the conduction band(s), while corrections due to virtual excitations into bands away from the Fermi surface are typically neglected. Here, using a functional renormalization group approach, we present an improved truncation for the treatment of the effective interactions in the conduction band that keeps track of the generated three-particle interactions (six-point term) and hence allows one to include important aspects of these virtual interband excitations. Within a simplified two-patch treatment of the conduction band, we demonstrate that these corrections can have a rather strong effect in parts of the phase diagram by changing the critical scales for various orderings and the phase boundaries.

Umklapp Scattering in Fermi Liquids: A Renormalisation Group Approach

The role of Umklapp scattering for electrons on a lattice is studied. Using renormalisation group methods it is shown that the effective low energy interaction involves not only forward scattering, but also non-forward Umklapp scattering. We show that the latter can happen to almost all of the electrons even when they have a filling of around one-half. The bahavior of these Umklapp couplings is studied in the loop expansion. It is shown that they remain marginal to all loop orders. The discussion is given in the context of two-dimensional lattices, but generalisation to three-dimensions is mentioned. We also briefly discuss the possible consequences of this on Fermi liquid theory and on physical properties of such electronic systems.

Pseudogaps and shadow bands in antiferromagnetically correlated metals

We provide a detailed numerical comparison between various approaches to the problem of antiferromagnetically correlated metals. We study the strength of the shadow band peak in the spectral function and the depth of the pseudogap in the density of states as a function of the spin-fluctuation spectrum. We show that a well developed pseudogap and a strong shadow band peak should only be experimentally observable for large antiferromagnetic enhancements of the effective low-energy interaction. {copyright} {ital 1997} {ital The American Physical Society}

Hilbert space of wormholes.

Wormhole boundary conditions for the Wheeler-DeWitt equation can be derived from the path integral formulation. It is proposed that the wormhole wave function must be square integrable in the maximal analytic extension of minisuperspace. Quantum wormholes can be invested with a Hilbert-space structure, the inner product being naturally induced by the minisuperspace metric, in which the Wheeler-DeWitt operator is essentially self-adjoint. This provides us with a kind of probabilistic interpretation. In particular, giant wormholes will give extremely small contributions to any wormhole state. We also study the whole spectrum of the Wheeler-DeWitt operator and its role in the calculation of Green's functions and effective low-energy interactions.

Lepton-Hadron interactions from supersymmetry radiative corrections

The new particles and interactions implied by supersymmetric theories may induce, via radiative corrections, new effective low energy interactions in the “standard” sector of the theory. We calculate the effects of lepton-hadron “contact” interactions thus induced as they appear in the π ℓ2 decay and in the energy levels of hydrogenic atoms (induced Lamb shift).

A confining SU(2) L × SU(2) R gauge model of the weak interactions

With the aim of understanding weak interactions as residual hypercolor interactions among composite quarks and leptons, we investigate a confining SU(2) L × SU(2) R hypercolor gauge theory with only fundamental fermions (i.e. without fundamental scalars). A scenario with two different confinement scales, Λ L ∼ G F − 1 2 ∼ 300 GeV and Λ R > Λ L, is systematically analyzed as a function of the parameter ξ = Λ R/ Λ L. The general requirement of anomaly saturation is combined with effective lagrangian techniques—a powerful procedure also of interest for more general confining product groups. Two solutions, separated by a phase boundary, emerge. Phase I for 1 ⩽ ξ < ξ crit: a left-right symmetric spectrum of massless composite quarks and leptons with a possibility for dominance of V-A effective low-energy interactions. Phase II for ξ > ξ crit: only left-handed massless composite quarks and leptons (of the Abbott-Farhi type). Phase II results from separate anomaly saturation at the two scales Λ R and Λ L, Phase I from joint anomaly saturation (matching). Dynamical insight comes from treating confinement in two steps, at Λ R and Λ L consecutively, which amounts to a complementary version of the technicolor mechanism; it necessarily entails the appearance of Goldstone bosons in the intermediate momentum range, Λ < p < Λ R, which play the rôle of dynamical scalars being subject to SU(2) L confinement.

ρ→ππin the SLAC lattice quantum-chromodynamic theory

Using the SLAC lattice Hamiltonian QCD theory, we compute the decay width for the decay width for the decay rho/sup +/..--> pi../sup +/..pi../sup 0/. There is reasonable agreement between the theoretical result and observation. There are two key ingredients involved in our calculation. One is the vacuum-insertion technique of Lee, Primack, and Treiman for the evaluation of light-hadron matrix elements of effective low-energy interaction densities. The other is the identification of the SLAC lattice currents with the physical hadron currents to leading order in the SLAC order-1/g/sup 2/ effective Hamiltonian for the fluxless light-hadron sector: in the spirit of Gell-Mann's work in current algebra. Our result suggests that the SLAC theory, taken together with these two ingredients, provides a viable technique for calculating large-distance light-hadron dynamics.