Mott insulators

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Mott insulators

Mott insulators

Atomic limit - view electrons in real space

Virtual system:

lattice of H-Atoms:

a B


Mott insulators

Atomic limit - view electrons in real space

Virtual system:

2a B

lattice of H-Atoms:

d

a B


Mott insulators

Atomic limit - view electrons in real space

Virtual system:

lattice of H-Atoms:

a B


Mott insulators

Metal-insulator transition from the insulating side

Hubbard-model:

density: n=1

„ground state“

n.n. hopping

t = 0

onsite repulsion

E

charge excitation

U

h

d


Mott insulators

Metal-insulator transition from the insulating side

Hubbard-model:

density: n=1

„ground state“

n.n. hopping

onsite repulsion

t > 0

W = 4d t

E

charge excitation

U

h

d

metal-insulator transition: U c = 4dt


Mott insulators

Metal-insulator transition from the metallic side

tight-binding model

h

d

half-filled

conduction

band

density

empty sites h = 1/4

doubly occupied sites d = 1/4

singly occupied sites s = 1/2

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

h

density of doubly occupied sites

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

factor

uncorrelated

analogous with same g t

d changed, not in sector


Mott insulators

Gutzwiller approximation

Metal-insulator transition from the metallic side

correlated

renormalization

factor

uncorrelated

minimize w.r.t. d

per site

Brinkmann-Rice (1970)


Mott insulators

Gutzwiller approximation

optical conductivity:

Drude weight

quasiparticle weight:

single particle spectral function

A

coherent

quasiparticles

metallic

variational

at MIT

A

lower

Hubbard band

upper

Hubbard band

E

insulating

µ

renormalized hopping E


Mott insulators

Gutzwiller approximation

Fermi liquid properties within Gutzwiller approximation:

renormalized

momentum

distribution

n k

Z

k

Gutzwiller

n k

n in

Z

n out

k

k F

k F

half-filling

renormalized hopping

particle-hole symmetry


Mott insulators

Gutzwiller approximation

Fermi liquid properties within Gutzwiller approximation:

renormalized

momentum

distribution

n k

Z

k

Gutzwiller

n k

n in

Z

n out

k

k F

k F

quasiparticle weight

compressibility

half-filling

half-filling

renormalized hopping

renormalized hopping

particle-hole symmetry

particle-hole symmetry

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