Large N expansion of the infinite U two-dimensional Hubbard model

We introduce a hierarchy of closed equations for charge density correlation functions in the Hubbard model and $2 + 1$ dimensional QED. Each step in the hierarchy can be considered a large $N$ truncation of an exact, but infinite set of equations relating all $k-$ point charge correlators. $N$ is the number of fermion spin components. Each step in the hierarchy sums up an infinite number of large $N$ diagrams, including all diagrams up to some fixed order, for $k$ point functions with $k \leq K$ . Higher point functions are replaced with their leading large $N$ behavior. The simplest truncation gives a closed nonlinear equation for the $2$ point function.We introduce a hierarchy of closed equations for charge density correlation functions in the Hubbard model and $2 + 1$ dimensional QED. Each step in the hierarchy can be considered a large $N$ truncation of an exact, but infinite set of equations relating all $k-$point charge correlators. $N$ is the number of fermion spin components. Each step in the hierarchy sums up an infinite number of large $N$ diagrams, including all diagrams up to some fixed order, for $k$ point functions with $k \leq K$. Higher point functions are replaced with their leading large $N$ behavior. The simplest truncation gives a closed nonlinear equation for the $2$ point function.

arXiv:2003.13136Mar 29, 20200 citations

Energy spectrum of the two-dimensional Hubbard model with infinite repulsion

Yuliya V. Mikhailova

Journal of Experimental and Theoretical PhysicsMar 1, 19960 citations

Systematic 1/d Corrections to the Infinite-Dimensional Limit of Correlated Lattice Electron Models

Avraham Schiller, Kevin Ingersent

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

We introduce a hierarchy of closed equations for charge density correlation functions in the Hubbard model and

2 + 1

dimensional QED. Each step in the hierarchy can be considered a large

N

truncation of an exact, but infinite set of equations relating all

k-

point charge correlators.

N

is the number of fermion spin components. Each step in the hierarchy sums up an infinite number of large

N

diagrams, including all diagrams up to some fixed order, for

k

point functions with

k \leq K

. Higher point functions are replaced with their leading large

N

behavior. The simplest truncation gives a closed nonlinear equation for the

2

point function.

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