@@ -167,7 +167,8 @@ and $Q_{\vR}=(R_\vR^+R_\vR^- - R_\vR^-R_\vR^+)=1$~(-1) for vortex~(antivortex) a

% LARGE MASS

{\em Large mass limit.--} First insights are obtained from the limit $|\mu| \gg J_{x,y}$, which, in contrast to the two-leg QLM~\cite{supmat}~\nocite{aklt, Pollmann2010, Pollmann2012, Pollmann2012A}, is different

{\em Large mass limit.--} First insights are obtained from the limit $|\mu| \gg J_{x,y}$, which, in contrast to the two-leg QLM~\cite{supmat}, is different

Title = {{\rm See {Supplementary Material}, which includes Refs.~\cite{aklt, Pollmann2010, Pollmann2012, Pollmann2012A}, for detailed numerical results and extended data on the RK-states and string-tension calculations.}}

Title = {{\rm See {Supplementary Material}, which includes Refs.~\cite{aklt, Pollmann2010, Pollmann2012, Pollmann2012A}, for detailed numerical results and extended data on the RK-states and string-tension calculations, and on the simplified 1D model of Eq. (2).}}

}

@manual{DMRGnote,

...

...

@@ -351,11 +351,13 @@ and Desbuquois, R{\'e}mi

and Messer, Michael

and Esslinger, Tilman},

title={Realization of density-dependent Peierls phases to engineer quantized gauge fields coupled to ultracold matter},

\usepackage{dcolumn}% Align table columns on decimal point

\usepackage{bm}% bold math

\usepackage{graphicx}

%\usepackage{pdfsync}

%\usepackage{showkeys}

\usepackage{color}

\usepackage{version}

\newcommand{\qref}[1]{``\textit{#1}''}

...

...

@@ -27,12 +25,15 @@ Dear Editors,

\vspace{2mm}

We hereby resubmit our revised paper ``Deconfining disordered phase in two-dimensional quantum link models'' (LL16725) for publication in Physical Review Letters.

Thank you very much for communicating to us the referee reports and we also thank both referees for their careful reading and detailed and constructive comments. We are pleased to read that both referees consider our work "important", "interesting for different fields of researchers", and "suitable for

publication in PRL" after some improvements. As the referees highlight the newly discovered D-phase with some resemblance to spin-liquid physics could be very interesting for on-going quantum gas experiments.

We would like to thank both referees for their careful reading of our manuscript and their detailed and constructive comments. We are pleased to read that both referees consider

our work "important", "interesting for different fields of researchers", and "suitable for

publication in PRL" after some improvements. As the referees highlight, the newly discovered D-phase, which bears some resemblance to spin-liquid physics, could be very interesting

for on-going quantum gas experiments.

\vspace{2mm}

Please find below our detailed reply to the referees. The extensions and modifications done to the resubmitted manuscript are listed in bold text, in correspondence to our answers to specific points. We hope that, with these modifications, the paper will be suitable for publication in Physical Review Letters.

Please find below our detailed reply to the referees. Motivated by the comments and questions of the referees, we have introduced some extensions and modifications in the resubmitted

manuscript and in the supplementary material, which we detail below. We hope that with these modifications the paper is now suitable for publication in Physical Review Letters.

\vspace{2mm}

...

...

@@ -49,7 +50,7 @@ L. Cardarelli, S. Greschner and L. Santos

\item demonstration of the stability of the DMRG-procedure with bond-dimension in new Fig. S6

\item excitation gap calculation for various models in new Fig. S7

\item updated discussion of the classical Metropolis sampling in the SM

\item discussion of the symmetries of the 1D-toy model and calculation of the generalized topological order parameter

\item discussion of the symmetries of the 1D-toy model and calculation of the generalized topological order parameter in the SM

\item several corrected typos, updated references

\end{itemize}

...

...

@@ -261,8 +262,8 @@ Even though analytical calculations seem possible, the numerical sampling of the

matrix. In the future work we will try to extend our numerical DMRG method to more 2D-settings on larger cylinders, and here a comparison with analytical results will be indeed an interesting objective.

As mentioned above, also in our Metropolis sampling we do not mix symmetry sectors.

Initialization of the system in a random gauge symmetry sector can be interpreted a random localized charges to the problem. This can lead to interesting localization and dynamical effects as discussed in Ref.[34].

In this work we limit our discussion to the interesting physics of the gauge vacuum sector, which is a good case to start - maybe also for experiments, which typically also would probably fix the gauge sector. Furthermore, as the referee pointed out above, there are some interesting connections to the quantum dimer models (a special case of two localized defects is actually shown in the paper while discussion the string tension).

Initialization of the system in a random gauge symmetry sector can be interpreted as random localized charges to the problem. This can lead to interesting localization and dynamical effects as discussed in Ref.[34].

In this work we limit our discussion to the interesting physics of the gauge vacuum sector, which is a good case to start - maybe also for experiments, which typically also would probably fix the gauge sector. Furthermore, as the referee pointed out above, there are some interesting connections to the quantum dimer models (a special case of two localized defects is actually shown in the paper in our discussion of the string tension).

Hence, the physics in different gauge sectors will be an interesting problem, but we believe that this goes beyond the scope of the present work.