The Tomonaga–Luttinger–Liquid (TLL) has been the cornerstone of our understanding of the properties of one dimensional systems. This universal set of properties plays in one dimension, the same role than Fermi liquid plays for the higher dimensional metals. I will give in these notes an overview of some of the experimental tests that were made to probe such TLL physics. In particular I will detail some of the recent experiments that were made in spin systems and which provided remarkable quantitative tests of the TLL physics.
We theoretically study the properties of the photo-carriers created in a one-dimensional Mott insulator subject to strong AC electric fields. The time-dependent density matrix renormalization group method is used to calculate the nonlinear optical conductivity, for which a metallic, gapless mode is found to emerge. The mode has linear dispersion with a charge velocity that differs from the free electron velocity, which indicates that the photo-doped carriers behave collectively as in the Tomonaga-Luttinger liquid.
Photoinduced metallic states in a Mott insulator are studied for the half-filled one-dimensional Hubbard model with the time-dependent density-matrix renormalization group. An irradiation of strong ac fields is found to create, in the nonequilibrium steady state, a linear dispersion in the optical spectrum (current-current correlation) reminiscent of the Tomonaga-Luttinger liquid for the doped Mott insulator in equilibrium. The spin spectrum in nonequilibrium retains the des Cloizeaux--Pearson mode with the spin velocity differing from the charge velocity. The mechanism of the photocarrier doping, along with the renormalization in the charge velocity, is analyzed in terms of an effective Dirac model.