Dynamic response of 1D fermions Dynamic response of 1D fermions - - PowerPoint PPT Presentation

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Dynamic response of 1D fermions Dynamic response of 1D fermions - - PowerPoint PPT Presentation

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Dynamic response of 1D fermions Dynamic response of 1D fermions Michael Pustilnik Michael Pustilnik in collaboration with Leonid Glazman Leonid Glazman Alex Kamenev Alex Kamenev U. of Minnesota Maxim Khodas Maxim Khodas Dynamics and

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Michael Pustilnik Michael Pustilnik

in collaboration with

Dynamic response of 1D fermions Dynamic response of 1D fermions

Leonid Glazman Leonid Glazman Alex Kamenev Alex Kamenev Maxim Khodas Maxim Khodas

  • U. of Minnesota

Dynamics and Relaxation in Complex Quantum and Classical Systems and Nanostructures

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Outline Outline

  • introduction
  • solvable model 2
  • solvable model 1
  • perturbation theory

M.P., PRL 97, 036404 (2006) M.P. et al., PRL 97, 196405 (2006)

  • beyond perturbation theory

(free fermions) (Calogero-Sutherland)

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Introduction Introduction

Landau’s Fermi liquid theory (1956): excitations of strongly interacting system of fermions excitations of free Fermi gas a liquid of weakly interacting quasiparticles how well the quasiparticles are defined? spectral function Lorentzian

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Failure of perturbation theory in 1D Failure of perturbation theory in 1D

Dzyaloshinskii, Larkin (1973) exact for linear spectrum

FL’s particles/holes are not ‘good’ quasiparticles in 1D

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Elementary excitations in 1D Elementary excitations in 1D

1D: only collective excitations

  • waves of density (sound waves) - bosons

dynamic structure factor: proper quantity is now density-density cor. function

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Interacting 1D fermions: Interacting 1D fermions: RPA RPA

Dzyaloshinskii & Larkin (1973)

exact for linear spectrum

Do bosons make ‘better’ quasiparticles in 1D than quasiparticles/holes are in 3D Fermi liquid?

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Motivation Motivation

Challenge: how to account for interaction and nonlinearity

  • f spectrum simultaneously?

Applications Coulomb drag PRL 91, 126805 (2003)

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Motivation Motivation

Challenge: how to account for interaction and nonlinearity

  • f spectrum simultaneously?

Applications Inelastic neutron scattering off antiferromagnetic spin chains (maps to structure factor

  • f 1D spinless fermions)
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Free electrons Free electrons

Lehmann (Golden rule – like) representation

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Free electrons Free electrons

  • the peak is narrow– good news!

but… •

  • it is not a Lorentzian
  • (non-perturbative in curvature)
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Calogero Calogero-

  • Sutherland model

Sutherland model

elementary excitations

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Calogero Calogero-

  • Sutherland model

Sutherland model

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Calogero Calogero-

  • Sutherland model

Sutherland model

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Calogero Calogero-

  • Sutherland model

Sutherland model

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Calogero Calogero-

  • Sutherland model

Sutherland model

! !

  • this observation allows the evaluation of the integral
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Calogero Calogero-

  • Sutherland model

Sutherland model

see PRL 97, 036404 (2006)

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Calogero Calogero-

  • Sutherland model

Sutherland model

the exponents are 1st order in the interaction strength

the exponents

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Perturbation theory: bosons Perturbation theory: bosons

bosonization: nonlinearity as a perturbation:

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Perturbation theory: fermions Perturbation theory: fermions

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Perturbation theory: Perturbation theory: ω ω > > ω ω+

+

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Perturbation theory: Perturbation theory: ω ω-

  • <

< ω ω < < ω ω+

+

V

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Back to Calogero Back to Calogero-

  • Sutherland model

Sutherland model

V

bingo go!

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Fermi edge singularity in metals Fermi edge singularity in metals

Mahan (1967) Nozieres & De Dominicis (1969)

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Back to structure factor Back to structure factor

  • cf. edge singularity
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Back to structure factor Back to structure factor

important states:

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Beyond perturbation theory Beyond perturbation theory

important states:

the idea: project all other states out!

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Beyond perturbation theory Beyond perturbation theory

effective two-band model:

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Beyond perturbation theory Beyond perturbation theory

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Including the left Including the left-

  • movers

movers… …

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Including the left Including the left-

  • movers (results)

movers (results)

see PRL 97, 196405 (2006)

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AFM AFM spin chain spin chain -

  • numerics

numerics

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Coulomb drag Coulomb drag

PRL 91, 126805 (2003)

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AFM AFM spin chain spin chain

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Conclusions Conclusions

  • a challenge:

simultaneous account for interactions & nonlinear dispersion in a system of 1D fermions dynamic structure factor (density-density cor. function) single-particle cor. function fermions with spin

PRL 97, 036404 (2006) PRL 97, 196405 (2006) more is coming soon…

Dynamics and Relaxation in Complex Quantum and Classical Systems and Nanostructures