LUTTINGER LIQUID LUTTINGER LIQUID Speaker Iryna Kulagina T. Giamarchi “Quantum Physics in One Dimension” (Oxford, 2003) J. Voit “One-Dimensional Fermi Liquids” arXiv:cond-mat/9510014 Nichols T. Bronn “Luttinger Liquids” G. F. Giuliani and G. Vignale “Quantum Theory of the Electron Liquids” (Cambridge, 2005)
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LUTTINGER LIQUID Speaker Iryna Kulagina T. Giamarchi “Quantum Physics in One Dimension” (Oxford, 2003) J. Voit “One-Dimensional Fermi Liquids” arXiv:cond-mat/9510014.
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LUTTINGER LIQUIDLUTTINGER LIQUID
Speaker Iryna Kulagina
T. Giamarchi “Quantum Physics in One Dimension” (Oxford, 2003)
J. Voit “One-Dimensional Fermi Liquids” arXiv:cond-mat/9510014
Nichols T. Bronn “Luttinger Liquids”G. F. Giuliani and G. Vignale “Quantum Theory of the
Electron Liquids” (Cambridge, 2005)
Fermi GasFermi GasEnergy for single particle
Hamiltonian ( )
Elementary excitation:
1) addition of a particle at wavevector k (δnk=1),
energy
2) destruction of a particle at wavevector k (δnk=-1),
energy
2
2
2m k
k
2
2F
F
kE
m ( 0)FE T
k kk
H n k k
Fk k
0k k
Fk k0k k
Landau’s Fermi Liquid Landau’s Fermi Liquid Theory Theory
Physical propertiesPhysical propertiesThe Specific heat
The specific heat coefficient
Spin susceptibility
Compressibility
11
( )C T T
0
1
2F Fv v
u u
0
Fv
u
0
Fv K
u
ConclusionsConclusionsThe important properties of ID liquides:a continuous momentum distribution function n(k), varying with as |k−kF|α with an interaction-dependent exponent α, and a pseudogap in the single-particle density of states ∝|ω|α, consequences of the non-existence of fermionic quasi-particlessimilar power-law behaviour in all correlation functions, specifically in those for superconducting and spin or charge density wave fluctuations, with universal scaling relations between the different nonuniversal exponents, which depend only on one effective coupling constant per degree of freedomfinite spin and charge response at small wavevectors, and a finite Drude weight in the conductivitycharge-spin separationpersistent currents quantized in units of 2kF