Correlation effects in Low-Dimensional       Fermion Systems
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Correlation effects in Low-Dimensional Fermion Systems. Reza Asgari. Some examples. 1) Correlations in Electron Liquid - Low density - Low Dimensionality - Transports effects 2) Bose Einstein Condensation in Low dimension

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Correlation effects in Low-Dimensional Fermion Systems

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Correlation effects in Low-Dimensional Fermion Systems

Reza Asgari


Some examples

1)Correlations in Electron Liquid

- Low density

- Low Dimensionality

- Transports effects

2) Bose Einstein Condensation in Low dimension

- 1D cold atom in optical lattice

- BEC-BSC Crossover

3) Localization in correlated disorder Low dimension

- disorder/interaction?

- dimensionality and Anderson impurity

4) Strongly correlated in electronic structure

- L(S)DFT ( Weakly interaction)

- DMFT , LDA+DMFT ( Mediate interaction)

- LDA+U ( Insulator system)


Outline

1)Correlations in Electron Liquid

- Introduction

- Luttinger Liquid, Bosonization

2) Bose Einstein Condensation in Atomic Fermi Gases

- Introduction

- BEC-BSC Crossover

- Pairing Gap in Strongly Interacting Fermi Gas

- Pairing Without Superfluidity

- HTSC and Ultracold Atomic Fermi Gases


General Properties

Total Hamiltonian

Electron-electron interaction

Fourier transformation

of the Coulomb potentials


Density in D dimension

Or , more explicitly

Fermi wave vector

G. Giuliani and G. Vignale “ Quantum theory of the Electron Liquid” Cambridge 2005


Ground state energy: Kinetic, Exchange and Correlation

K.E :

XC. E :


Jellium Model: High density region,

Correlation

Ceperley & Alder, PRL 45, 566 (1980)


paramagnetic to fully spin-polarized quantum phase transition of a 2D EL

TC: B. Tanatar and D. M. Ceperley, Phys. Rev. B 39, 5005 (1989)

RS: F. Rapisarda and G. Senatore, Aust. J. Phys. 49, 161 (1996)

AMGB : C. Attaccalite, et al., Phys. Rev. Lett 88, 256601 (2002)

R. Asgari, B. Davoudi and M. P. Tosi, Solid State Communication 131,1(2004)


One Dimensional Electron System

  • Fermi Liquid Theory?

  • Divergent behavior ?

  • Perturbation Theory?

  • How to solve?

  • Bosonization


Strongly interacting system

Weakly interacting system


Fermi Liquid versus Non-Fermi Liquid


Particle-Hole Excitations

  • 2D system

  • 1D system


Most efficient processes in the interaction

For spinless fermions

Corresponding to spins

directions :


Vertex Interactions and renormalization velocity

Solyom 1979


Bosonization


Density fluctuation and boson fields

Y is the step function


Fermion fields in terms of boson operators


Spinless Fermion: Interactions


Spinless 1D net Hamiltonian


Thermodynamics


Compressibility


Correlations


Green’s Function


Occupation number


Many Body effects 1D system

arises from the variation of the Bose expression of the ground state energy respect to g(r)

The Induced exchange potential arises from the Fermi part

The exact ground state wave-function of a Bose system

The four- and five- body elementary diagrams

(1): L. J. Lantto and P. J. Siemens, Nucl. Phys. A 317, 55 (1979)(2): A. Kallio and J. Piilo, Phys. Rev. Lett. 77, 4237 (1996)

(3): B. Davoudi et al., Phys. Rev. B 68, 155112 (2003) and series of our works


Numerical Results

R. Asgari SSC 141, 563 (2007)


Correlation energy in comparison with DMC

R. Asgari SSC 141, 563 (2007)


End of 2th Lecture

Thank you for your attention


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