# Optical response in two model systems of interacting electrons: The 1D Hubbard model and 2D magnetoexcitons

## Abstract

In Part I of this thesis, we study the real part {sigma}({omega}) of the optical conductivity of a repulsive Hubbard ring of circumference L. At zero temperature, and in the absence of disorder, the dc part of {sigma}({omega}) has the form {sigma}({omega}) = (e{sup 2}/h)D{sub c}{delta}({h_bar}{omega}). The charge stiffness D{sub c} tends to a finite, positive value as L {yields} {infinity} in the metallic phase of the model; however, in the Mott-insulating phase of the model, which occurs at a mean electron density n = 1 (half filling), D{sub c} {approximately} O(L{sup 1/2}exp(-L/{xi}(U)) in the large-L limit, which serves to define the localization length {xi} of the nondisordered Mott insulator. We obtain an analytic expression for {xi}(U) as a function of the on-site repulsion U, and show that {xi} is the correlation length of the equal-time single-particle Green`s function, evaluated at half filling. We interpret {xi} as the correlation length of the electron-hole pairing correlations in the ground state of the Mott insulator. We next consider the metallic phase of the model in the vicinity of the metal-insulator transition. We obtain analytic expressions, valid to leading order in the doping {delta} = {vert_bar}1 - n{vert_bar}, for the charge stiffness D{submore »

- Authors:

- Publication Date:

- Research Org.:
- Princeton Univ., NJ (United States)

- OSTI Identifier:
- 114807

- Resource Type:
- Miscellaneous

- Resource Relation:
- Other Information: TH: Thesis (Ph.D.); PBD: 1992

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; HUBBARD MODEL; ELECTRON CORRELATION; MOTT SCATTERING; EXCITONS; GREEN FUNCTION; ELECTRON-HOLE COUPLING; ELECTRICAL INSULATORS; ELECTRON DENSITY

### Citation Formats

```
Stafford, C A.
```*Optical response in two model systems of interacting electrons: The 1D Hubbard model and 2D magnetoexcitons*. United States: N. p., 1992.
Web.

```
Stafford, C A.
```*Optical response in two model systems of interacting electrons: The 1D Hubbard model and 2D magnetoexcitons*. United States.

```
Stafford, C A. Thu .
"Optical response in two model systems of interacting electrons: The 1D Hubbard model and 2D magnetoexcitons". United States.
```

```
@article{osti_114807,
```

title = {Optical response in two model systems of interacting electrons: The 1D Hubbard model and 2D magnetoexcitons},

author = {Stafford, C A},

abstractNote = {In Part I of this thesis, we study the real part {sigma}({omega}) of the optical conductivity of a repulsive Hubbard ring of circumference L. At zero temperature, and in the absence of disorder, the dc part of {sigma}({omega}) has the form {sigma}({omega}) = (e{sup 2}/h)D{sub c}{delta}({h_bar}{omega}). The charge stiffness D{sub c} tends to a finite, positive value as L {yields} {infinity} in the metallic phase of the model; however, in the Mott-insulating phase of the model, which occurs at a mean electron density n = 1 (half filling), D{sub c} {approximately} O(L{sup 1/2}exp(-L/{xi}(U)) in the large-L limit, which serves to define the localization length {xi} of the nondisordered Mott insulator. We obtain an analytic expression for {xi}(U) as a function of the on-site repulsion U, and show that {xi} is the correlation length of the equal-time single-particle Green`s function, evaluated at half filling. We interpret {xi} as the correlation length of the electron-hole pairing correlations in the ground state of the Mott insulator. We next consider the metallic phase of the model in the vicinity of the metal-insulator transition. We obtain analytic expressions, valid to leading order in the doping {delta} = {vert_bar}1 - n{vert_bar}, for the charge stiffness D{sub c} = {delta}/{vert_bar}2m{sup *}{vert_bar} and the low-temperature thermopower S = -(k{sup 2}{sub B}T/3e)m{sup *}/{delta}{sup 2} near half filing, where {vert_bar}m{sup *}{vert_bar} is a function of U which we calculate, and sign(m{sup *}) = sign(1 - n). We interpret these results in terms of a physical picture of the charge carriers in the lightly doped Mott insulator as spinless fermionic solitons of size {xi}, effective mass m{sup *}, and number density {delta}, which become noninteracting in the limit {xi}{delta} {yields} 0.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1992},

month = {12}

}