The set of particle-hole ring diagrams for a many-fermion system in two dimensions is studied. The complex-valued polarization function is derived in detail and shown to be expressible in terms of square-root functions. For a contact-interaction the perturbative contributions to the energy per particle $\bar E(k_f)$ are calculated in closed analytical form from third up to twelfth order. The resummation of the particle-hole ring diagrams to all orders is studied and a pronounced dependence on the dimensionless coupling parameter $\alpha$ is found. There is a substantial difference between the complete ring-sum with all exchange-type diagrams included and the standard resummation of the leading $n$ -ring diagrams only. The spin factor $S_n(g)$ associated to the $n$ -th order ring diagrams is derived for arbitrary spin-degeneracy $g$ .The set of particle-hole ring diagrams for a many-fermion system in two dimensions is studied. The complex-valued polarization function is derived in detail and shown to be expressible in terms of square-root functions. For a contact-interaction the perturbative contributions to the energy per particle $\bar E(k_f)$ are calculated in closed analytical form from third up to twelfth order. The resummation of the particle-hole ring diagrams to all orders is studied and a pronounced dependence on the dimensionless coupling parameter $\alpha$ is found. There is a substantial difference between the complete ring-sum with all exchange-type diagrams included and the standard resummation of the leading $n$-ring diagrams only. The spin factor $S_n(g)$ associated to the $n$-th order ring diagrams is derived for arbitrary spin-degeneracy $g$.

Aug 17, 20162 citations

Variational and parquet-diagram calculations for neutron matter. IV. Spin-orbit interactions and linear response

E. Krotscheck, Jiawei Wang

We develop the parquet-diagram summation method for neutron matter interacting via potentials that include spin, tensor, and spin-orbit components. For that purpose, we derive an exact expression for the sum of all ring diagrams in terms of effective local particle-hole interactions involving the above four operators. The parquet equations are closed by deriving the spin-orbit contribution to those particle-hole interactions. We show that many-body correlations screen the bare spin-orbit potential considerably, and the corrections of that screened spin-orbit potential to the other three interaction channels are quite small. We apply our method to the calculation of the response of neutron matter to density and both longitudinal and transverse spin-dependent external fields.We develop the parquet-diagram summation method for neutron matter interacting via potentials that include spin, tensor, and spin-orbit components. For that purpose, we derive an exact expression for the sum of all ring diagrams in terms of effective local particle-hole interactions involving the above four operators. The parquet equations are closed by deriving the spin-orbit contribution to those particle-hole interactions. We show that many-body correlations screen the bare spin-orbit potential considerably, and the corrections of that screened spin-orbit potential to the other three interaction channels are quite small. We apply our method to the calculation of the response of neutron matter to density and both longitudinal and transverse spin-dependent external fields.

arXiv:2111.12051Physical Review CMar 30, 20227 citations

The Two-Particle Picture and Electronic Structure Calculations

Antonios Gonis, T. C. Schulthess, P. E. A. Turchi

Springer eBooksJan 1, 19990 citations

Communication: Random-phase approximation excitation energies from approximate equation-of-motion coupled-cluster doubles

Timothy C. Berkelbach

The ground-state correlation energy calculated in the random-phase approximation (RPA) is known to be identical to that calculated using a subset of terms appearing in coupled-cluster theory with double excitations (CCD). In particular, for particle-hole (ph) RPA this equivalence requires keeping only those terms that generate time-independent ring diagrams, and for particle-particle (pp) RPA it requires keeping only those terms that generate ladder diagrams. Here I show that these identities extend to excitation energies, for which those calculated in each RPA are identical to those calculated using approximations to equation-of-motion coupled-cluster theory with double excitations (EOM-CCD). The equivalence requires three approximations to EOM-CCD: first, the ground-state CCD amplitudes are obtained from the ring-CCD or ladder-CCD equations (the same as for the correlation energy); second, the EOM eigenvalue problem is truncated to the minimal subspace, which is one particle + one hole for ph-RPA and two particles or two holes for pp-RPA; third, the similarity transformation of the Fock operator must be neglected, as it corresponds to a Brueckner-like dressing of the single-particle propagator, which is not present in the conventional RPA.The ground-state correlation energy calculated in the random-phase approximation (RPA) is known to be identical to that calculated using a subset of terms appearing in coupled-cluster theory with double excitations (CCD). In particular, for particle-hole (ph) RPA this equivalence requires keeping only those terms that generate time-independent ring diagrams, and for particle-particle (pp) RPA it requires keeping only those terms that generate ladder diagrams. Here I show that these identities extend to excitation energies, for which those calculated in each RPA are identical to those calculated using approximations to equation-of-motion coupled-cluster theory with double excitations (EOM-CCD). The equivalence requires three approximations to EOM-CCD: first, the ground-state CCD amplitudes are obtained from the ring-CCD or ladder-CCD equations (the same as for the correlation energy); second, the EOM eigenvalue problem is truncated to the minimal subspace, which is one particle + one hole for ph-RPA and two particles or two holes for pp-RPA; third, the similarity transformation of the Fock operator must be neglected, as it corresponds to a Brueckner-like dressing of the single-particle propagator, which is not present in the conventional RPA.

arXiv:1804.01037The Journal of Chemical PhysicsJul 28, 201832 citations

\bar E(k_f)

are calculated in closed analytical form from third up to twelfth order. The resummation of the particle-hole ring diagrams to all orders is studied and a pronounced dependence on the dimensionless coupling parameter

\alpha

is found. There is a substantial difference between the complete ring-sum with all exchange-type diagrams included and the standard resummation of the leading

n

-ring diagrams only. The spin factor

S_n(g)

associated to the

n

-th order ring diagrams is derived for arbitrary spin-degeneracy

g