Tomonaga-Luttinger parameters for quantum wires -: art. no. 085104

The low-energy properties of a homogeneous one-dimensional electron system are completely specified by two Tomonaga-Luttinger parameters K-rho and upsilon(sigma) In this paper we discuss microscopic estimates of the values of these parameters in semiconductor quantum wires that exploit their relationship to thermodynamic properties. Motivated by the recognized similarity between correlations in the ground state of a one-dimensional electron liquid and correlations in a Wigner crystal, we evaluate these thermodynamic quantities in a self-consistent Hartree-Fock approximation. According to our calculations, the Hartree-Fock approximation ground state is a Wigner crystal at all electron densities and has antiferromagnetic order that gradually evolves from spin-density wave to localized in character as the density is lowered. Our results for K-rho are in good agreement with weak-coupling perturbative estimates K-rho(pert) at high densities, but deviate strongly at low densities, especially when the electron-electron interaction is screened at long distances. K(rho)(pert)similar ton(1/2) vanishes at small carrier density it, whereas we conjecture that K-rho-->1/2 when n-->0, implying that K-rho should pass through a minimum at an intermediate density. Observation of this nonmonotonic dependence could be used to measure the effective interaction range in a realistic semiconductor quantum wire geometry. In the spin sector we find that the spin velocity decreases with increasing interaction strength or decreasing n. Strong correlation effects make it difficult to obtain fully consistent estimates of upsilon(sigma) from Hartree-Fock calculations. We conjecture that, upsilon(sigma)/upsilon(F)proportional ton/V-0 where V-0 is the interaction strength, in the limit n-->0.