# Extremely correlated Fermi liquids in the limit of infinite dimensions

## Abstract

We study the infinite spatial dimensionality limit (d→∞) of the recently developed Extremely Correlated Fermi Liquid (ECFL) theory (Shastry 2011, 2013) [17,18] for the t–J model at J=0. We directly analyze the Schwinger equations of motion for the Gutzwiller projected (i.e. U=∞) electron Green’s function G. From simplifications arising in this limit d→∞, we are able to make several exact statements about the theory. The ECFL Green’s function is shown to have a momentum independent Dyson (Mori) self energy. For practical calculations we introduce a partial projection parameter λ, and obtain the complete set of ECFL integral equations to O(λ{sup 2}). In a related publication (Zitko et al. 2013) [23], these equations are compared in detail with the dynamical mean field theory for the large U Hubbard model. Paralleling the well known mapping for the Hubbard model, we find that the infinite dimensional t–J model (with J=0) can be mapped to the infinite-U Anderson impurity model with a self-consistently determined set of parameters. This mapping extends individually to the auxiliary Green’s function g and the caparison factor μ. Additionally, the optical conductivity is shown to be obtainable from G with negligibly small vertex corrections. These results are shown to holdmore »

- Authors:

- Publication Date:

- OSTI Identifier:
- 22224239

- Resource Type:
- Journal Article

- Journal Name:
- Annals of Physics (New York)

- Additional Journal Information:
- Journal Volume: 338; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONTROL; CORRECTIONS; ELECTRON CORRELATION; ELECTRONS; EQUATIONS OF MOTION; FERMI GAS; FUNCTIONS; HUBBARD MODEL; INTEGRAL EQUATIONS; MAPPING; MEAN-FIELD THEORY; SELF-ENERGY

### Citation Formats

```
Perepelitsky, Edward, and Sriram Shastry, B.
```*Extremely correlated Fermi liquids in the limit of infinite dimensions*. United States: N. p., 2013.
Web. doi:10.1016/J.AOP.2013.09.010.

```
Perepelitsky, Edward, & Sriram Shastry, B.
```*Extremely correlated Fermi liquids in the limit of infinite dimensions*. United States. https://doi.org/10.1016/J.AOP.2013.09.010

```
Perepelitsky, Edward, and Sriram Shastry, B. Fri .
"Extremely correlated Fermi liquids in the limit of infinite dimensions". United States. https://doi.org/10.1016/J.AOP.2013.09.010.
```

```
@article{osti_22224239,
```

title = {Extremely correlated Fermi liquids in the limit of infinite dimensions},

author = {Perepelitsky, Edward and Sriram Shastry, B.},

abstractNote = {We study the infinite spatial dimensionality limit (d→∞) of the recently developed Extremely Correlated Fermi Liquid (ECFL) theory (Shastry 2011, 2013) [17,18] for the t–J model at J=0. We directly analyze the Schwinger equations of motion for the Gutzwiller projected (i.e. U=∞) electron Green’s function G. From simplifications arising in this limit d→∞, we are able to make several exact statements about the theory. The ECFL Green’s function is shown to have a momentum independent Dyson (Mori) self energy. For practical calculations we introduce a partial projection parameter λ, and obtain the complete set of ECFL integral equations to O(λ{sup 2}). In a related publication (Zitko et al. 2013) [23], these equations are compared in detail with the dynamical mean field theory for the large U Hubbard model. Paralleling the well known mapping for the Hubbard model, we find that the infinite dimensional t–J model (with J=0) can be mapped to the infinite-U Anderson impurity model with a self-consistently determined set of parameters. This mapping extends individually to the auxiliary Green’s function g and the caparison factor μ. Additionally, the optical conductivity is shown to be obtainable from G with negligibly small vertex corrections. These results are shown to hold to each order in λ. -- Highlights: •Infinite-dimensional t–J model (J=0) studied within new ECFL theory. •Mapping to the infinite U Anderson model with self consistent hybridization. •Single particle Green’s function determined by two local self energies. •Partial projection through control variable λ. •Expansion carried out to O(λ{sup 2}) explicitly.},

doi = {10.1016/J.AOP.2013.09.010},

url = {https://www.osti.gov/biblio/22224239},
journal = {Annals of Physics (New York)},

issn = {0003-4916},

number = ,

volume = 338,

place = {United States},

year = {2013},

month = {11}

}