1. 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)

2. Fermi Gas Energy for single particle Hamiltonian ( ) Elementary excitation: 1) addition of a particle at wavevector k (δn k =1), energy 2) destruction of a particle at wavevector k (δn k =-1), energy 2

3. Landau’s Fermi Liquid Theory Adding a particle Destructing a particle Ground state quasiparticle distribution Changing of quasiparticle occupation number Energy change Expansion of energy Energy of quasiparticle added to the system 3

4. Particle-Hole Excitations 4

5. Luttinger Liquid. Noninteracting problem 5 Hamiltonian Linear spectrum New Hamiltonian Spectrum

6. Bozonization Fourier components of the particle density operators Commutation relations for operators Commutation relations for Hamiltonian Hamiltonian 6

7. Interacting Hamiltonian Excitation spectrum Field operators Commutation relations 7

8. Interacting Hamiltonian Full Hamiltonian Parameters Current density 8

9. Model with spin Kinetic energy Where Interacting Hamiltonians 9

10. Model with spin Full Hamiltonian Where with 10

11. Physical properties The Specific heat The specific heat coefficient Spin susceptibility Compressibility 11

12. Conclusions The important properties of ID liquides: a continuous momentum distribution function n(k), varying with as |k − k F | 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-particles similar 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 freedom finite spin and charge response at small wavevectors, and a finite Drude weight in the conductivity charge-spin separation persistent currents quantized in units of 2k F 12

13. Thank you for attention 13