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

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 Relaxation in Complex Quantum and Classical Systems and Nanostructures

Outline Outline • introduction • • solvable model 1 • (free fermions) • solvable model 2 • (Calogero-Sutherland) • perturbation theory • • beyond perturbation theory • M.P., PRL 97 , 036404 (2006) M.P. et al ., PRL 97 , 196405 (2006)

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

Failure of perturbation theory in 1D Failure of perturbation theory in 1D exact for linear spectrum Dzyaloshinskii, Larkin (1973) FL’s particles/holes are not ‘good’ quasiparticles in 1D

Elementary excitations in 1D Elementary excitations in 1D 1D : only collective excitations - waves of density (sound waves) - bosons proper quantity is now density-density cor. function dynamic structure factor:

Interacting 1D fermions: RPA RPA Interacting 1D fermions: exact for linear spectrum Dzyaloshinskii & Larkin (1973) Do bosons make ‘better’ quasiparticles in 1D than quasiparticles/holes are in 3D Fermi liquid?

Motivation Motivation Challenge: how to account for interaction and nonlinearity of spectrum simultaneously? Applications Coulomb drag PRL 91 , 126805 (2003)

Motivation Motivation Challenge: how to account for interaction and nonlinearity of spectrum simultaneously? Applications Inelastic neutron scattering off antiferromagnetic spin chains (maps to structure factor of 1D spinless fermions)

Free electrons Free electrons Lehmann (Golden rule – like) representation

Free electrons Free electrons • the peak is narrow– good news! • • it is not a Lorentzian but… • ( non-perturbative in curvature) • •

-Sutherland model Sutherland model elementary excitations Calogero- Calogero

Calogero- -Sutherland model Sutherland model Calogero

Calogero- -Sutherland model Sutherland model Calogero

Calogero- -Sutherland model Sutherland model Calogero

Calogero- -Sutherland model Sutherland model Calogero ! ! - this observation allows the evaluation of the integral

Calogero- -Sutherland model Sutherland model Calogero see PRL 97 , 036404 (2006)

Calogero- -Sutherland model Sutherland model Calogero the exponents the exponents are 1st order in the interaction strength

Perturbation theory: bosons Perturbation theory: bosons bosonization : nonlinearity as a perturbation:

Perturbation theory: fermions Perturbation theory: fermions

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

ω - ω < ω + Perturbation theory: ω < ω < ω Perturbation theory: - < + V

Back to Calogero- -Sutherland model Sutherland model Back to Calogero V go! bingo

Fermi edge singularity in metals Fermi edge singularity in metals Mahan (1967) Nozieres & De Dominicis (1969)

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

Back to structure factor Back to structure factor important states:

Beyond perturbation theory Beyond perturbation theory important states: the idea: project all other states out!

Beyond perturbation theory Beyond perturbation theory effective two-band model:

Beyond perturbation theory Beyond perturbation theory

Including the left- -movers movers… … Including the left

Including the left- -movers (results) movers (results) Including the left see PRL 97 , 196405 (2006)

AFM spin chain spin chain - - numerics numerics AFM

PRL 91 , 126805 (2003) Coulomb drag Coulomb drag

AFM spin chain spin chain AFM

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 PRL 97 , 036404 (2006) fermions with spin PRL 97 , 196405 (2006) more is coming soon… Dynamics and Relaxation in Complex Quantum and Classical Systems and Nanostructures