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Correlation effects in Low-Dimensional Fermion SystemsPowerPoint Presentation

Correlation effects in Low-Dimensional Fermion Systems

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Presentation Transcript

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)

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

Total Hamiltonian

Electron-electron interaction

Fourier transformation

of the Coulomb potentials

Or , more explicitly

Fermi wave vector

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

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

Weakly interacting system

- 2D system
- 1D system

Most efficient processes in the interaction

For spinless fermions

Corresponding to spins

directions :

Vertex Interactions and renormalization velocity

Solyom 1979

Density fluctuation and boson fields

Y is the step function

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

R. Asgari SSC 141, 563 (2007)

Correlation energy in comparison with DMC

R. Asgari SSC 141, 563 (2007)

Thank you for your attention

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