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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

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Presentation Transcript
slide3

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)

slide4

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

slide5

General Properties

Total Hamiltonian

Electron-electron interaction

Fourier transformation

of the Coulomb potentials

slide6

Density in D dimension

Or , more explicitly

Fermi wave vector

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

slide8

Jellium Model: High density region,

Correlation

Ceperley & Alder, PRL 45, 566 (1980)

slide9

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)

slide10

One Dimensional Electron System

  • Fermi Liquid Theory?
  • Divergent behavior ?
  • Perturbation Theory?
  • How to solve?
  • Bosonization
slide11

Strongly interacting system

Weakly interacting system

slide13

Particle-Hole Excitations

  • 2D system
  • 1D system
slide14

Most efficient processes in the interaction

For spinless fermions

Corresponding to spins

directions :

slide28

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

slide29

Numerical Results

R. Asgari SSC 141, 563 (2007)

slide30

Correlation energy in comparison with DMC

R. Asgari SSC 141, 563 (2007)

slide31

End of 2th Lecture

Thank you for your attention

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