Power-Law Dependence of Correlaration Functions in the Tomonaga-Luttinger Liquid
Nelson Oyindenyifa Nenuwe, Famous Akpojotor
The power-law dependence of correlation functions at low energies is what clearly distinguishes the Tomonaga-Luttinger (TL) liquid and the Fermi liquid (FL). The correlation function critical exponent for the FL is usually fixed to an integer, while that of the TL liquid varies continuously. We calculate the nature of power-law dependence in the charge, spin and electron correlation functions for the TL liquid at both zero and small magnetic fields. In particular, our approach centres on the Bethe Ansatz and conformal field theory (CFT). This is important since the concept of CFT relates critical exponents of various correlation functions with the finite-size corrections to the energy spectrum. Our findings show that increase in the particle density nc, and external magnetic field B, increases the value of the critical exponents while increase in the interaction strength u, decreases the value of the critical exponents.
International Journal of Theoretical and Mathematical Physics•Jan 1, 2015•1 citation