Commit 77dd16bf authored by Jefferson Stafusa E. Portela's avatar Jefferson Stafusa E. Portela
Browse files

Stub of new tutorial version.

parent b17a66cf
......@@ -18,9 +18,9 @@
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\providecommand\BKM@entry[2]{}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces $\Delta \tau t $ extrapolation for the 4-site Hubbard ring. }}{2}{figure.1}\protected@file@percent }
\@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}\protected@file@percent }
\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}}
\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}{}}
\@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}\protected@file@percent }
\@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}}
\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}{}}
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% Copyright (c) 2016 The ALF project.
% Copyright (c) 2016-2020 The ALF project.
% This is the ALF project documentation.
% The ALF project documentation by the ALF contributors is licensed
% under a Creative Commons Attribution-ShareAlike 4.0 International License.
......@@ -110,7 +110,9 @@
\section*{Introduction}
The ALF package provides a general code for auxiliary-field Quantum Monte Carlo simulations and default analysis. In this tutorial we show how users from beginners to specialists can profit from ALF.
In the first part of the tutorial we make use of ALF's python interface
\section*{Downloading the code and tutorial}
To download the code, type \texttt{ git clone git@git.physik.uni-wuerzburg.de:ALF/ALF\_code.git} in a shell. \\
......@@ -122,7 +124,7 @@ Run the code with the Mz choice of Hubbard Stratonovitch transformation on a fo
\langle -t \sum_{\langle i,j\rangle, \sigma} c_{i,\sigma}^{\dagger} c_{j,\sigma}^{\phantom\dagger} + U \sum_{i=1}^{N} n_{i,\uparrow}n_{j,\downarrow} \rangle = -1.47261997 t
\end{equation}
To reproduce this result you will have to carry out a systematic $\Delta \tau t $ extrapolation keeping $\Delta \tau t L_{\text Trotter} = 2$ constant.
To reproduce this result you will have to carry out a systematic $\Delta \tau t $ extrapolation keeping $\Delta \tau t L_\text{Trotter} = 2$ constant.
Recall that the formulation of the auxiliary field QMC approach is based on the Trotter decomposition
\begin{equation}
e^{-\Delta \tau \left( A + B \right ) } = e^{-\Delta \tau A } e^{-\Delta \tau B } + {\cal O} \left( \Delta \tau^2 \right)
......
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