Accurate localization of Kosterlitz-Thouless-type quantum phase transitions for one-dimensional spinless fermions

Spinless fermions in one dimension with nearest-neighbor transfer amplitude $\ensuremath{-}t$ and interaction $V$ display a Kosterlitz-Thouless-type quantum phase transition from a Luttinger liquid metal to a charge density wave insulator at finite interaction strength ${V}_{\mathrm{c}}=2t$. The authors use the density matrix renormalization group (DMRG) method on rings with $L\ensuremath{\le}512$ sites for an accurate localization of the transition. The maximum of the quasiparticle density in the upper Hartree-Fock band, ${n}_{\ensuremath{\beta}}^{\mathrm{max}}(L,V)={\mathrm{max}}_k\phantom{\rule{0.167em}{0ex}}{n}_{k,\ensuremath{\beta}}(L,V)$, develops a peak close to the critical interaction whose position extrapolates to the exact result in the thermodynamic limit, ${lim}_{L\ensuremath{\rightarrow}\mathrm{\ensuremath{\infty}}}{V}_{\ensuremath{\beta}}^{\mathrm{max}}(L,V)={V}_{\mathrm{c}}$, with an accuracy of better than one percent. Monitoring the Luttinger parameter permits to locate the transition with an accuracy of three percent.