"Phenomenology of 1D quantum liquids beyond low energy limit"

Adilet Imambekov

Yale University

We consider zero temperature behavior of dynamic response functions of 1D systems near edges of support in momentum-energy plane $(k, \omega).$ Description of singularities of dynamic response functions near an edge $\varepsilon(k)$ is given by the effective Hamiltonian of a mobile impurity moving in a Luttinger liquid. In the vicinity of Fermi points nonlinearity of the function $\varepsilon(k)$ leads to qualitative change in the behavior of the spectral function compared to predictions of Luttinger liquid theory. Away from Fermi points we derive phenomenological relations for the parameters of effective Hamiltonians irrespective of the details of microscopic interactions. Combined with Galilean invariance, it allows to express the exponents for spinless bosonic or fermionic liquids as simple functions of $\varepsilon(k)$ and Luttinger liquid parameters.

References: arXiv:0812.1046 (accepted to PRL); Science 323, 228 (2009);

Phys. Rev. Lett. 100, 206805 (2008).