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

Interacting Fermions in 2 Dimensions

Vincent Rivasseau

Lecture notes in physicsJan 1, 20060 citations

Fermion Systems in Different Dimensions

Leon N. Cooper

Springer eBooksJan 1, 19770 citations

Comparison of two methods for calculating finite-temperature ring diagrams

Shen Yang, Meng Jiang, T.T.S. Kuo +1 more

Certain types of ring diagrams of the thermodynamic potential \ensuremath{\Omega} can be summed up to all orders using two apparently very different methods---the eigenvalue method and the transition-amplitude method. A relatively simple derivation of these methods is given, and we show that these two methods are exactly equivalent to each other. To study their numerical applications we have calculated the particle-particle, hole-hole ring diagrams of \ensuremath{\Omega} for nuclear matter with both methods, using a modified Gogny interaction. Our results suggest that the strength-parameter integration involved in the transition-amplitude method can be accurately performed using a small number of mesh points and both methods seem to be suitable for numerical calculations.Certain types of ring diagrams of the thermodynamic potential \ensuremath{\Omega} can be summed up to all orders using two apparently very different methods---the eigenvalue method and the transition-amplitude method. A relatively simple derivation of these methods is given, and we show that these two methods are exactly equivalent to each other. To study their numerical applications we have calculated the particle-particle, hole-hole ring diagrams of \ensuremath{\Omega} for nuclear matter with both methods, using a modified Gogny interaction. Our results suggest that the strength-parameter integration involved in the transition-amplitude method can be accurately performed using a small number of mesh points and both methods seem to be suitable for numerical calculations.

Physical Review CAug 1, 19892 citations

Effect of ring exchange on an orbital antiferromagnet

C. H. Chung, Hae‐Young Kee, Yong Baek Kim

We study the effect of four-particle ring exchange process on an orbital antiferromagnetic state that occurs in some correlated electron systems in two dimensions. The primary question is whether the ring exchange process enhances or suppresses the orbital antiferromagnetic ordering. Using the fact that the orbital antiferromagnetic state arises in the large- $N$ limit of the $\mathrm{SU}(N)$ generalization of the $t\ensuremath{-}J$ model, we consider the large- $N$ limit of the $t\ensuremath{-}J\ensuremath{-}K$ model where K represents the four-particle ring exchange term. The phase diagrams in the large- $N$ mean-field theory are obtained for the half-filling and finite hole concentrations at zero temperature. It is found that the ring exchange in general favors dimerized states or the inhomogeneous orbital antiferromagnetic state and suppresses the homogeneous orbital antiferromagnetic state. We compare our results with other related models of strongly correlated systems with ring exchange processes.We study the effect of four-particle ring exchange process on an orbital antiferromagnetic state that occurs in some correlated electron systems in two dimensions. The primary question is whether the ring exchange process enhances or suppresses the orbital antiferromagnetic ordering. Using the fact that the orbital antiferromagnetic state arises in the large-$N$ limit of the $\mathrm{SU}(N)$ generalization of the $t\ensuremath{-}J$ model, we consider the large-$N$ limit of the $t\ensuremath{-}J\ensuremath{-}K$ model where K represents the four-particle ring exchange term. The phase diagrams in the large-$N$ mean-field theory are obtained for the half-filling and finite hole concentrations at zero temperature. It is found that the ring exchange in general favors dimerized states or the inhomogeneous orbital antiferromagnetic state and suppresses the homogeneous orbital antiferromagnetic state. We compare our results with other related models of strongly correlated systems with ring exchange processes.

arXiv:cond-mat/0211299Physical review. B, Condensed matterJun 10, 20035 citations

Interacting fermions on a one-channel ring

Fedor Vasilievich Kusmartsev

Physics Letters AJan 1, 199236 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

N

limit of the

\mathrm{SU}(N)

generalization of the $t\ensuremath{-}J$ model, we consider the large-

N

limit of the $t\ensuremath{-}J\ensuremath{-}K$ model where K represents the four-particle ring exchange term. The phase diagrams in the large-

N

mean-field theory are obtained for the half-filling and finite hole concentrations at zero temperature. It is found that the ring exchange in general favors dimerized states or the inhomogeneous orbital antiferromagnetic state and suppresses the homogeneous orbital antiferromagnetic state. We compare our results with other related models of strongly correlated systems with ring exchange processes.