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