ALF_Tutorial.aux 3.2 KB
 Jefferson Stafusa E. Portela committed Aug 10, 2020 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 \relax \providecommand\hyper@newdestlabel[2]{} \providecommand\zref@newlabel[2]{} \providecommand*\new@tpo@label[2]{} \providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} \HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined \global\let\oldcontentsline\contentsline \gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} \global\let\oldnewlabel\newlabel \gdef\newlabel#1#2{\newlabelxx{#1}#2} \gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} \AtEndDocument{\ifx\hyper@anchor\@undefined \let\contentsline\oldcontentsline \let\newlabel\oldnewlabel \fi} \fi} \global\let\hyper@last\relax \gdef\HyperFirstAtBeginDocument#1{#1} \providecommand\HyField@AuxAddToFields[1]{} \providecommand\HyField@AuxAddToCoFields[2]{}  Jefferson Stafusa E. Portela committed Aug 14, 2020 21 22 23 \providecommand\tcolorbox@label[2]{} \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces $\Delta \tau t$ extrapolation for the 4-site Hubbard ring. }}{2}{figure.1}} \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Spin correlation functions along one leg for the Hubbard ladder. As $t_y$ grows the spin gap becomes large enough so as to detect the exponential decal of the spin correlation function on this small lattice size. The underlying physics of odd-even ladder systems is introduced in the article: Elbio Dagotto and T. M. Rice, Surprises on the way from one- to two-dimensional quantum magnets: The ladder materials, Science 271 (1996), no. 5249, 618?623. }}{5}{figure.2}}  Jefferson Stafusa E. Portela committed Aug 10, 2020 24 \newlabel{Ladder.fig}{{2}{5}{Spin correlation functions along one leg for the Hubbard ladder. As $t_y$ grows the spin gap becomes large enough so as to detect the exponential decal of the spin correlation function on this small lattice size. The underlying physics of odd-even ladder systems is introduced in the article: Elbio Dagotto and T. M. Rice, Surprises on the way from one- to two-dimensional quantum magnets: The ladder materials, Science 271 (1996), no. 5249, 618?623}{figure.2}{}}  Jefferson Stafusa E. Portela committed Aug 14, 2020 25 \@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Density-Density correlation functions of the t-V model. In the Luttinger liquid phase, $-2 < V/t < 2$ it is known that the density -density correlations decay as $\delimiter "426830A n(r) n(0)\delimiter "526930B \propto \qopname \relax o{cos}(\pi r) r^{-\left (1+K_\rho \right ) }$ with $\left (1+K_\rho \right )^{-1}= \frac {1}{2} + \frac {1}{\pi } \qopname \relax o{arcsin}\left ( \frac {V}{2 | t | }\right )$ (A. Luther and I. Peschel, Calculation of critical exponents in two dimensions from quantum field theory in one dimension, Phys. Rev. B 12 (1975), 3908.) The interested reader can try to reproduce this result. }}{6}{figure.3}}  Jefferson Stafusa E. Portela committed Aug 10, 2020 26 \newlabel{tV.fig}{{3}{6}{Density-Density correlation functions of the t-V model. In the Luttinger liquid phase, $-2 < V/t < 2$ it is known that the density -density correlations decay as $\langle n(r) n(0)\rangle \propto \cos (\pi r) r^{-\left (1+K_\rho \right ) }$ with $\left (1+K_\rho \right )^{-1}= \frac {1}{2} + \frac {1}{\pi } \arcsin \left ( \frac {V}{2 | t | }\right )$ (A. Luther and I. Peschel, Calculation of critical exponents in two dimensions from quantum field theory in one dimension, Phys. Rev. B 12 (1975), 3908.) The interested reader can try to reproduce this result}{figure.3}{}}