The Haldane hypothesis about the universality of the Luttinger liquid (LL) behavior in conducting one-dimensional fermion systems is checked numerically for the spinless fermion model with next-nearest-neighbor interactions. It is shown that for the large enough interactions the ground state can be gapless due to frustrations but at the same time might not belong to the same universality class as a simple LL. The exponents of the correlation functions for this unusual conducting state are found numerically by a finite-size method.
The thermopower
SL(T) of a finite Luttinger liquid (LL) wire containing an impurity and connected to leads of noninteracting electrons is calculated. It is shown that at low temperatures ${k}_{B}T\ensuremath{\ll}{\ensuremath{\Delta}}_{L}\ensuremath{\simeq}\ensuremath{\Elzxh}{\mathbf{v}}_{F}/gL$ (L is the length of the wire,
vF is the Fermi velocity of the electrons, and g is the correlation parameter of the LL),
SL(T) is described by a Mott-type formula. However, at higher temperatures, that is, when ${\ensuremath{\Delta}}_{L}<~{k}_{B}T\ensuremath{\ll}{\ensuremath{\varepsilon}}_{F},$ the expression for
SL(T) contains an interaction-dependent factor. For strong interelectron interaction, the enhancement of the thermopower is large and it is much more pronounced for spinless electrons.