Fermi liquid theory 1 Concept of Landau's Fermi liquid theory elementary excitations of interacting Fermions are described by almost independent fermionic quasiparticles state of Fermi liquid described simply by quasiparticle distribution Phenomenological Theory by Landau energy functional: deviation from ground state ground state distribution filled Fermi sea spin index
Fermi liquid theory 2 effective quasiparticle spectrum: bare quasiparticle spectrum: Fermi velocity: effective mass density of states at : Fermi volume conserved
Fermi liquid theory 3 couplings: antisymmetric symmetric (spin) (charge) spherical symmetry: Legendre Polynomials Landau parameters: charge spin
Fermi liquid theory - physical properties 4 specific heat: T thermal softening of Fermi surface compressibility: change of Fermi volume spin susceptibility: spin splitting of Fermi sea
Fermi liquid theory - Gallilei invariance 5 momentum shift for all particles current density shifted Fermi sea ''bare particle'' view quasiparticle view quasiparticle induced motion motion intrinsic consistency
Fermi liquid theory - 3 He Fermi liquid 6 strong short-range repulsion Fermi liquid longer-ranged attraction superfluid enhanced diminished enhanced
Fermi liquid theory Microscopic considerations 7 Hamiltonian kinetic energy contact interaction „perturbation “ Rayleigh-Schrödinger Fermi liquid theory perturbation theory Landau parameters
Fermi liquid theory Microscopic considerations 8 Rayleigh-Schrödinger energy: Distribution function characterizes unperturbed state
Fermi liquid theory Microscopic considerations 9 Rayleigh-Schrödinger
Fermi liquid theory Microscopic considerations 10 Rayleigh-Schrödinger Fermi sea
Fermi liquid theory Microscopic considerations 11 Rayleigh-Schrödinger „screening “ cutoff interaction range Fermi sea weak K -dependence
Fermi liquid theory Microscopic considerations 12 Rayleigh-Schrödinger cancels relabeling
Fermi liquid theory Microscopic considerations 13 Rayleigh-Schrödinger
Fermi liquid theory Microscopic considerations 14 Rayleigh-Schrödinger variation:
Fermi liquid theory Microscopic considerations 15
Fermi liquid theory Microscopic considerations 16 Lindhard function
Fermi liquid theory Microscopic considerations 17 Lindhard function
Fermi liquid theory Microscopic considerations 18
Fermi liquid theory Microscopic considerations 19
Fermi liquid theory Microscopic considerations 20
Fermi liquid theory Microscopic considerations 21 Landau parameters:
Fermi liquid theory Microscopic considerations 22 Landau parameters: repulsive interaction
Fermi liquid theory Microscopic considerations 23 repulsive interaction higher more spin less compressible effective mass polarizable ferromagnetism
Fermi liquid theory Microscopic considerations 24 distribution function ground state
Fermi liquid theory Microscopic considerations 25 distribution function 3-dimensional Fermigas
Fermi liquid theory Microscopic considerations 26 distribution function quasiparticle Z weight
Fermi liquid theory one-dimensional systems 27 Landau parameters breakdown of perturbation approach !
Fermi liquid theory one-dimensional systems 28 distribution function 1-dimensional Fermigas non-perturbative
Fermi liquid theory one-dimensional systems 29 distribution function non-perturbative 1-dimensional Fermigas no quasiparticle Tomonaga weight Luttinger Z=0 not a Fermi liquid liquid
Fermi liquid theory one-dimensional systems 30 Tomonaga-Luttinger liquid no quasiparticles Fermi liquid behavior disappears Z=0 excitations: collective modes (bosonization of Fermions) separation of charge and spin excitations charge spin
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