Fermi-Luttinger Liquid Michael Pustilnik, Georgia Tech

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Presentation transcript:

Fermi-Luttinger Liquid Michael Pustilnik, Georgia Tech 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 … M. Chang, et al 1996 Dekker et al 1997 Bockrath, et al 1997 Auslaender et al 2004 I. Bloch 2004

Spectral Function

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

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

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

Luttinger model (cont) Haldane, 1983

1D with non-linear dispersion: Holes

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

Particles (cont) Fermi head with the Luttinger tail

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

Structure Factor

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

Spectrum curvature + interactions Fourier components of the interaction potential V

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

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

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

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.

Summary of bosonic exponents Boson-Fermion mapping Hydrodynamics ?

Numerics (preliminary) Courtesy of J-S. Caux

Numerics (preliminary) Courtesy of J-S. Caux