Commit f0bb108f authored by Sebastian Greschner's avatar Sebastian Greschner

Merge branch 'master' of gitlab.unige.ch:Sebastian.Greschner/lgt2

parents baf87ce1 e16952c9
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......@@ -34,7 +34,7 @@
\bibcite{Shastry1981}{{1}{1981}{{Shastry\ and\ Sutherland}}{{}}}
\@writefile{lof}{\contentsline {figure}{\numberline {S6}{\ignorespaces Energy error $E_{\rm {err}} = E(\chi ) - E_0$ as a function of the bond dimension $\chi $, for different values of $J_y$ in the disordered region and close to the phase transitions (four-leg cylinder, $\mu =0$, L=40, DMRG results). $E_0$ is an estimate of the ground-state energy for a fixed chain length obtained by fitting the data with an exponential curve. }}{4}{}}
\newlabel{fig:energy_vs_chi}{{S6}{4}{}{}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {S7}{\ignorespaces Excitation gap $\Delta \epsilon $ (in units of $J_x$) for the (a) 1D toy model, (b) 2-leg (c) 4-leg ladder model within the vacuum gauge-sector at $\mu =0$ for different system sized $L=12$ (crosses), $L=24$ (circle), $L=36$ (plus-symbols). The dotted lines indicate the estimated phase-transition position from Tab.\nobreakspace {}I{}{}{}\hbox {}. (d) Excitation gap as function of the number of legs for $J_y / J_x=1$ (center of the D-phase) and $J_y/J_x=1.8$ (Sy-phase).}}{4}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {S7}{\ignorespaces Excitation gap $\Delta \epsilon $ (in units of $J_x$) for the (a) 1D toy model, (b) 2-leg (c) 4-leg ladder model within the vacuum gauge-sector at $\mu =0$ for different system sized $L=12$ (crosses), $L=24$ (circle), $L=36$ (plus-symbols). The dotted lines indicate the estimated phase-transition position from Tab.\nobreakspace {}I{}{}{}\hbox {}. (d) Excitation gap as a function of the number of legs for $J_y / J_x=1$ (center of the D-phase) and $J_y/J_x=1.8$ (Sy-phase).}}{4}{}}
\newlabel{fig:gap_legs}{{S7}{4}{}{}{}}
\@writefile{toc}{\contentsline {section}{\numberline {VIII}Extended data on the string tension}{4}{}}
\bibcite{Anderson1987}{{2}{1987}{{Anderson}}{{}}}
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......@@ -90,7 +90,7 @@ Traditionally, as in Refs.~\cite{Shastry1981,Anderson1987, Moessner2002, Ralko20
\begin{align}
H_{QDM} = \sum_\vR (R^+_\vR + R^-_\vR) + \lambda Q_{\vR}^2 \,.
\end{align}
On the square lattice this models have been shown to exhibit several phase transitions as function of $\lambda$: Phases found and discussed e.g. in Ref.~\cite{Tschirsich2019} are Neel, columnar, or a plaquette-ordered (also called RVB-solid) phase.
On the square lattice this models have been shown to exhibit several phase transitions as a function of $\lambda$: Phases found and discussed e.g. in Ref.~\cite{Tschirsich2019} are Neel, columnar, or a plaquette-ordered (also called RVB-solid) phase.
At the phase transition-point between columnar and plaquette-ordered phase, lies the so called Rokhsar-Kivelson point, which is discussed in the main text.
......@@ -309,7 +309,7 @@ $E_0$ is an estimate of the ground-state energy for a fixed chain length obtaine
\begin{figure}[tb]
\includegraphics[width=.99\linewidth]{gap_legs.pdf}
\caption{Excitation gap $\Delta \epsilon$ (in units of $J_x$) for the (a) 1D toy model, (b) 2-leg (c) 4-leg ladder model within the vacuum gauge-sector at $\mu=0$ for different system sized $L=12$ (crosses), $L=24$ (circle), $L=36$ (plus-symbols). The dotted lines indicate the estimated phase-transition position from Tab.~\ref{tab:S_transitions}.
(d) Excitation gap as function of the number of legs for $J_y / J_x=1$ (center of the D-phase) and $J_y/J_x=1.8$ (Sy-phase).}
(d) Excitation gap as a function of the number of legs for $J_y / J_x=1$ (center of the D-phase) and $J_y/J_x=1.8$ (Sy-phase).}
\label{fig:gap_legs}
\end{figure}
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