We present a self-consistent treatment of Hubbard-like lattice models at large, but finite, spatial dimensions $d$ . This involves a systematic expansion in powers of $1/d$ about the limit $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\infty}$. The first-order corrections can be obtained by self-consistent solution of coupled one- and two-impurity models. We calculate the leading corrections to properties of the Falicov-Kimball model. The infinite-dimensional limit seems to describe this particular model remarkably well even for $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ .We present a self-consistent treatment of Hubbard-like lattice models at large, but finite, spatial dimensions $d$. This involves a systematic expansion in powers of $1/d$ about the limit $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\infty}$. The first-order corrections can be obtained by self-consistent solution of coupled one- and two-impurity models. We calculate the leading corrections to properties of the Falicov-Kimball model. The infinite-dimensional limit seems to describe this particular model remarkably well even for $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$.

Physical Review LettersJul 3, 199571 citations

Infinite-Dimensional Algebras in Exactly Solvable Models of Strongly Correlated Electrons and Statistical Mechanics

Denis B. Uglov

Jan 1, 19950 citations

Study of strongly correlated electron systems in infinite dimensions

Dai S. Hirashima, 平島大

Jan 1, 19950 citations

Extremely correlated limit of the Hubbard model

Edward Perepelitsky

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

Finite Size Effects in Correlated Electron Models

Andrei A. Zvyagin

IMPERIAL COLLEGE PRESS eBooksMay 1, 200539 citations

We present a self-consistent treatment of Hubbard-like lattice models at large, but finite, spatial dimensions

d

. This involves a systematic expansion in powers of

1/d

about the limit $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\infty}$. The first-order corrections can be obtained by self-consistent solution of coupled one- and two-impurity models. We calculate the leading corrections to properties of the Falicov-Kimball model. The infinite-dimensional limit seems to describe this particular model remarkably well even for

d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2