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Fermi-Luttinger Liquid

Fermi-Luttinger Liquid. Alex Kamenev. in collaboration with. Leonid Glazman, U of M Maxim Khodas, U of M. Michael Pustilnik, Georgia Tech. PRL 96 , 196405 (2006); arXiv:cond-mat/0702.505 arXiv:cond-mat/0705.2015. RPMBT14, Jul., 2007. One-dimensional …. Dekker et al 1997.

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Fermi-Luttinger Liquid

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  1. Fermi-Luttinger Liquid Alex Kamenev in collaboration with Leonid Glazman, U of M Maxim Khodas, U of M Michael Pustilnik, Georgia Tech PRL 96, 196405 (2006); arXiv:cond-mat/0702.505 arXiv:cond-mat/0705.2015 RPMBT14, Jul., 2007

  2. One-dimensional … Dekker et al 1997 Bockrath, et al 1997 M. Chang, et al 1996 Auslaender et al 2004 I. Bloch 2004

  3. Spectral Function

  4. d>1: Fermi Liquid Spectral density: Energy relaxation rate: interaction potential • The same for holes

  5. Spectral density: Energy relaxation rate: d=1 ? ?

  6. Spectral density: Energy relaxation rate: Luttinger model Dzaloshinskii, Larkin 1973

  7. Luttinger model (cont) Haldane, 1983

  8. 1D with non-linear dispersion: Holes

  9. Energy relaxation rate: interaction potential 1D with non-linear dispersion: Particles • Does not work for integrable models

  10. Particles (cont) • Fermi head with the Luttinger tail

  11. Spectral Edges • Shake up or X-ray singularity (cf. Mahan, Nozieres,…)

  12. Structure Factor

  13. Linear dispersion • Exact result within the Luttinger approximation. Luttinger approximation How does the dispersion curvature and interactions affect the structure factor ?

  14. interactions Fourier components of the interaction potential V Spectrum curvature + interactions

  15. AFM spin chain N 200. For this case we have calculated 2 200 000 form factors S. Nagler, et al 2005

  16. Caux, Calabrese, 2006 Constant-q scan Lieb-Liniger model, 1963 Bose-Fermi mapping (1D) Bosons with the strong repulsion = Fermions with the weak attraction – changes sign. 1D hard-core bosons = free fermions (Tonks-Girardeau) Divergence at the upper edge 1D Bose Liquid

  17. Bosons Structure factor: conclusions • Power law singularities at the spectral edges (Lieb modes) with q-dependent exponents. Fermions

  18. Fermi-Luttinger Liquid • Hole’s mass-shell is described by the Luttinger liquid (with momentum-dependent exponent). • Particle’s mass-shell is described by the Fermi liquid (with smaller relaxation rate). • Spectral edges of the spectral function and the structure factor exhibit power-law singularities.

  19. Boson-Fermion mapping Hydrodynamics Summary of bosonic exponents ?

  20. Numerics (preliminary) Courtesy of J-S. Caux

  21. Numerics (preliminary) Courtesy of J-S. Caux

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