Mott insulators Atomic limit - view electrons in real space Virtual system: lattice of H-Atoms: aB << d 2aB d H Mott insulators Atomic limit - view electrons in real space lattice of H-Atoms: Virtual system: aB << d 2aB d hopping - electron transfer - H H + -t ionization energy H delocalization localization kinetic energy charge excitation energy metal Mott insulator Mott insulators Atomic limit - view electrons in real space lattice of H-Atoms: Virtual system: aB << d 2aB d hopping - electron transfer ionization energy H -t S = 1/2 Mott isolator effective low-energy model low-energy physics no charge fluctuation only spin fluctuation Mott insulators Metal-insulator transition from the insulating side Hubbard-model: n.n. hopping onsite repulsion density: n=1 „ground state“ t = 0 E charge excitation U h d Mott insulators Metal-insulator transition from the insulating side Hubbard-model: n.n. hopping onsite repulsion density: n=1 t > 0 „ground state“ E W = 4d t U charge excitation h d metal-insulator transition: Uc = 4dt Mott insulators Metal-insulator transition from the metallic side h d tight-binding model density empty sites h = 1/4 doubly occupied sites d = 1/4 half-filled singly occupied sites s = 1/2 conduction band reducing mobility Mott insulators Gutzwiller approximation Metal-insulator transition from the metallic side Gutzwiller-approach: variational diminish double-occupancy uncorrelated state variational groundstate density of doubly occupied sites renormalized hopping Mott insulators Gutzwiller approximation Metal-insulator transition from the metallic side densities: 1 electron density density of singly occupied sites with spin density of singly occupied sites with spin d density of doubly occupied sites h density of empty sites no spin polarization half-filling sum rule Mott insulators Gutzwiller approximation Metal-insulator transition from the metallic side hopping probability: sector of fixed d correlated renormalization uncorrelated factor analogous with same gt d changed, not in sector Mott insulators Gutzwiller approximation Metal-insulator transition from the metallic side correlated renormalization uncorrelated factor minimize w.r.t. d per site Brinkmann-Rice (1970) Mott insulators Gutzwiller approximation optical conductivity: Drude weight single particle spectral function coherent A quasiparticles metallic quasiparticle weight: variational lower upper E at MIT Hubbard band Hubbard band A insulating renormalizedµ hoppingE Mott insulators Gutzwiller approximation Fermi liquid properties within Gutzwiller approximation: n n k renormalized k Gutzwiller momentum Z nin Z distribution k nout k kF kF half-filling renormalized hopping particle-hole symmetry Mott insulators Gutzwiller approximation Fermi liquid properties within Gutzwiller approximation: n n k renormalized k Gutzwiller momentum Z nin Z distribution k nout k kF kF quasiparticle weight compressibility half-filling half-filling renormalized hopping renormalized hopping particle-hole symmetry particle-hole symmetry.