In this work, we describe the simplifications to the Extremely Correlated Fermi Liquid Theory (ECFL) \\cite{ECFL, Monster} which occur in the limit of infinite spatial dimensions. In particular, we show that the single-particle electron Green's function G(k) can be written in terms of two momentum-independent self-energies. Moreover, we elucidate the nature of the ECFL \\lambda expansion in the limit of infinite dimensions and carry out this expansion explicitly to O(\\lambda^2). Additionally, we demonstrate the vanishing of vertex corrections to the optical conductivity in general and to each order in \\lambda in the limit of infinite dimensions. We generalize the ECFL formalism to the infinite-U Anderson impurity model (AIM) , and demonstrate a Dynamical Mean-Field Theory (DMFT) like mapping between the ECFL objects of the infinite-dimensional t-J model and the infinite-U AIM, and show that this mapping holds to each order in \\lambda. We compute the spectral function for the AIM to O (\\lambda^2) and make comparisons with results obtained through Numerical Renormalization Group (NRG) computations. Finally, we develop a novel formalism for the high-temperature expansion of dynamical correlation functions in the infinite-U Hubbard model which is more efficient than any used previously and gives results for an arbitrary number of spin species. We use it to calculate the single-particle Green's function G(k) to fourth order in (\\beta t) for m spin-species on a d-dimensional hypercube.In this work, we describe the simplifications to the Extremely Correlated Fermi Liquid Theory (ECFL) \\cite{ECFL, Monster} which occur in the limit of infinite spatial dimensions. In particular, we show that the single-particle electron Green's function G(k) can be written in terms of two momentum-independent self-energies. Moreover, we elucidate the nature of the ECFL \\lambda expansion in the limit of infinite dimensions and carry out this expansion explicitly to O(\\lambda^2). Additionally, we demonstrate the vanishing of vertex corrections to the optical conductivity in general and to each order in \\lambda in the limit of infinite dimensions. We generalize the ECFL formalism to the infinite-U Anderson impurity model (AIM) , and demonstrate a Dynamical Mean-Field Theory (DMFT) like mapping between the ECFL objects of the infinite-dimensional t-J model and the infinite-U AIM, and show that this mapping holds to each order in \\lambda. We compute the spectral function for the AIM to O (\\lambda^2) and make comparisons with results obtained through Numerical Renormalization Group (NRG) computations. Finally, we develop a novel formalism for the high-temperature expansion of dynamical correlation functions in the infinite-U Hubbard model which is more efficient than any used previously and gives results for an arbitrary number of spin species. We use it to calculate the single-particle Green's function G(k) to fourth order in (\\beta t) for m spin-species on a d-dimensional hypercube.

Jan 1, 20140 citations

Extremely Correlated Fermi Liquid theory: Imposing the hole density sum-rule

B. Sriram Shastry

Bulletin of the American Physical SocietyMar 16, 20160 citations

Schwinger boson studies of the t-J model beyond mean-field approximation

Y. M. Li, Lei Yu, D. N. Sheng +1 more

Unknown eBooksDec 1, 19910 citations

Extremely correlated Fermi liquid theory for the U=∞, d=∞ Hubbard model to O(λ3)

S. Shears, Edward Perepelitsky, Michael Arciniaga +1 more

We present the $O({\ensuremath{\lambda}}^{3})$ results from the $\ensuremath{\lambda}$ expansion in the extremely correlated Fermi-liquid theory applied to the infinite-dimensional $t\ensuremath{-}J$ model (with $J=0$ ) and compare the results with the earlier $O({\ensuremath{\lambda}}^{2})$ results as well as the results from the dynamical mean-field theory. We focus attention on the $T$ dependence of the resistivity $\ensuremath{\rho}(T)$, the Dyson self-energy, and the quasiparticle weight $Z$ at various densities. The comparison shows that all the methods display quadratic-in- $T$ resistivity followed by a quasilinear-in- $T$ resistivity characterizing a strange metal and gives an estimate of the different scales of these variables relative to the exact results.We present the $O({\ensuremath{\lambda}}^{3})$ results from the $\ensuremath{\lambda}$ expansion in the extremely correlated Fermi-liquid theory applied to the infinite-dimensional $t\ensuremath{-}J$ model (with $J=0$) and compare the results with the earlier $O({\ensuremath{\lambda}}^{2})$ results as well as the results from the dynamical mean-field theory. We focus attention on the $T$ dependence of the resistivity $\ensuremath{\rho}(T)$, the Dyson self-energy, and the quasiparticle weight $Z$ at various densities. The comparison shows that all the methods display quadratic-in-$T$ resistivity followed by a quasilinear-in-$T$ resistivity characterizing a strange metal and gives an estimate of the different scales of these variables relative to the exact results.

arXiv:2204.08599Physical review. B./Physical review. BJul 6, 20222 citations

Strongly Correlated Fermion Systems and High-T Superconductivity.

Sudbo Asle

Jan 1, 19900 citations

J=0

) and compare the results with the earlier $O({\ensuremath{\lambda}}^{2})$ results as well as the results from the dynamical mean-field theory. We focus attention on the

T

dependence of the resistivity $\ensuremath{\rho}(T)$, the Dyson self-energy, and the quasiparticle weight

Z

at various densities. The comparison shows that all the methods display quadratic-in-

T

resistivity followed by a quasilinear-in-

T

resistivity characterizing a strange metal and gives an estimate of the different scales of these variables relative to the exact results.