Commit 9107643d authored by Sebastian Greschner's avatar Sebastian Greschner

updates

parent 222ce131
......@@ -66,7 +66,7 @@
\bibcite{Kasper2016}{{15}{2016}{{Kasper\ \emph {et~al.}}}{{Kasper, Hebenstreit, Oberthaler,\ and\ Berges}}}
\bibcite{Cardarelli2017}{{16}{2017}{{Cardarelli\ \emph {et~al.}}}{{Cardarelli, Greschner,\ and\ Santos}}}
\bibcite{Zache2018}{{17}{2018}{{Zache\ \emph {et~al.}}}{{Zache, Hebenstreit, Jendrzejewski, Oberthaler, Berges,\ and\ Hauke}}}
\bibcite{barbiero2018}{{18}{2018}{{Barbiero\ \emph {et~al.}}}{{Barbiero, Schweizer, Aidelsburger, Demler, Goldman,\ and\ Grusdt}}}
\bibcite{barbiero2018}{{18}{2019}{{Barbiero\ \emph {et~al.}}}{{Barbiero, Schweizer, Aidelsburger, Demler, Goldman,\ and\ Grusdt}}}
\bibcite{Martinez2016}{{19}{2016}{{Martinez\ \emph {et~al.}}}{{Martinez, Muschik, Schindler, Nigg, Erhard, Heyl, Hauke, Dalmonte, Monz, Zoller,\ and\ Blatt}}}
\bibcite{Bernien2017}{{20}{2017}{{Bernien\ \emph {et~al.}}}{{Bernien, Schwartz, Keesling, Levine, Omran, Pichler, Choi, Zibrov, Endres, Greiner, Vuletic,\ and\ Lukin}}}
\bibcite{Clark2018}{{21}{2018}{{Clark\ \emph {et~al.}}}{{Clark, Anderson, Feng, Gaj, Levin,\ and\ Chin}}}
......
......@@ -219,7 +219,7 @@
10.1088/2058-9565/aac33b} {\bibfield {journal} {\bibinfo {journal} {Quantum
Science and Technology}\ }\textbf {\bibinfo {volume} {3}},\ \bibinfo {pages}
{034010} (\bibinfo {year} {2018})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Barbiero}\ \emph {et~al.}(2018)\citenamefont
\bibitem [{\citenamefont {Barbiero}\ \emph {et~al.}(2019)\citenamefont
{Barbiero}, \citenamefont {Schweizer}, \citenamefont {Aidelsburger},
\citenamefont {Demler}, \citenamefont {Goldman},\ and\ \citenamefont
{Grusdt}}]{barbiero2018}%
......@@ -230,8 +230,9 @@
{author} {\bibfnamefont {E.}~\bibnamefont {Demler}}, \bibinfo {author}
{\bibfnamefont {N.}~\bibnamefont {Goldman}}, \ and\ \bibinfo {author}
{\bibfnamefont {F.}~\bibnamefont {Grusdt}},\ }\href@noop {} {\bibfield
{journal} {\bibinfo {journal} {arXiv preprint arXiv:1810.02777}\ } (\bibinfo
{year} {2018})}\BibitemShut {NoStop}%
{journal} {\bibinfo {journal} {Science advances}\ }\textbf {\bibinfo
{volume} {5}},\ \bibinfo {pages} {eaav7444} (\bibinfo {year}
{2019})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Martinez}\ \emph {et~al.}(2016)\citenamefont
{Martinez}, \citenamefont {Muschik}, \citenamefont {Schindler}, \citenamefont
{Nigg}, \citenamefont {Erhard}, \citenamefont {Heyl}, \citenamefont {Hauke},
......@@ -312,8 +313,8 @@
{N.}~\bibnamefont {Goldman}}, \bibinfo {author} {\bibfnamefont
{I.}~\bibnamefont {Bloch}}, \ and\ \bibinfo {author} {\bibfnamefont
{M.}~\bibnamefont {Aidelsburger}},\ }\href@noop {} {\bibfield {journal}
{\bibinfo {journal} {arXiv preprint arXiv:1901.07103}\ } (\bibinfo {year}
{2019})}\BibitemShut {NoStop}%
{\bibinfo {journal} {Nature Physics}\ }\textbf {\bibinfo {volume} {15}},\
\bibinfo {pages} {1168} (\bibinfo {year} {2019})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Mil}\ \emph {et~al.}(2019)\citenamefont {Mil},
\citenamefont {Zache}, \citenamefont {Hegde}, \citenamefont {Xia},
\citenamefont {Bhatt}, \citenamefont {Oberthaler}, \citenamefont {Hauke},
......
......@@ -28,43 +28,43 @@ Warning--empty year in Arrows
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......@@ -148,7 +148,7 @@ H = - \sum_{\vR,\vRp} J_{\vR,\vRp} \left( \psi_\vR^\dagger S^+_{\vR,\vRp} \psi_
\end{align}
% mu_r=mu for A and -mu for B. For mu>>0 piling on B, this means that B goes with -mu
where $\psi_\vR^\dagger$ is the fermionic operator at site $\vR$, and $n_\vR = \psi_\vR^\dagger \psi_\vR$.
In our case the gauge field is given by spin-$1/2$ operators $S^+_{\vR,\vRp}$ placed at the link between {\color{red}{two neighbouring}} sites $\vR$ and $\vRp$. The
In our case the gauge field is given by spin-$1/2$ operators $S^+_{\vR,\vRp}$ placed at the link between {{two neighbouring}} sites $\vR$ and $\vRp$. The
amplitudes $J_{\vR,\vR\pm\vX}=J_x$ and $J_{\vR,\vR\pm\vY}=J_y$ characterize, respectively, the hops along the $x$ and $y$ directions~(Fig.~\ref{fig:sketch}~(a)).
We enforce at each site the Gauss law $[H, G_\vR]=0$ with $G_\vR = \varepsilon_\vR - n_\vR + \sum_{\vec{k} \in \vX,\vY} ( S^z_{\vR,\vR+\vec{k}} - S^z_{\vR,\vR-\vec{k}} )$,
with $\varepsilon_{\vR\in A}=1$ and $\varepsilon_{\vR\in B}=0$.
......@@ -171,7 +171,7 @@ and $Q_{\vR}=(R_\vR^+R_\vR^- - R_\vR^-R_\vR^+)=1$~(-1) for vortex~(antivortex) a
for $\mu>0$ and $\mu<0$. For $\mu>0$, particles
are pinned in B sites~(Figs.~\ref{fig:sketch}~(b) and (c)).
Local states are characterized by the expectation value of two spin-$1$ operators, $S^z_{\vec{k}}(\vR) = S^z(\vR-\vec{k}, \vR) + $
{\color{red}{$S^z(\vR,\vR+\vec{k})$}},
{{$S^z(\vR,\vR+\vec{k})$}},
with $\vec{k}=\vX,\vY$.
For $J_x<J_y$, second-order terms select a ground-state manifold of two states with $S^z_y(\vR)=0$. Fourth-order ring-exchange $\propto J_x^2 J_y^2 / |\mu|^3$~\cite{Cardarelli2017}
favors a configuration of columns of flippable vortex-antivortex and non-flippable plaquettes~(Fig.~\ref{fig:sketch}~(b)). We denote this striped phase Sy.
......
......@@ -333,10 +333,14 @@ doi = {10.1080/00107514.2016.1151199},
}
@article{barbiero2018,
title={Coupling ultracold matter to dynamical gauge fields in optical lattices: From flux-attachment to Z2 lattice gauge theories},
title={Coupling ultracold matter to dynamical gauge fields in optical lattices: From flux attachment to ℤ2 lattice gauge theories},
author={Barbiero, Luca and Schweizer, Christian and Aidelsburger, Monika and Demler, Eugene and Goldman, Nathan and Grusdt, Fabian},
journal={arXiv preprint arXiv:1810.02777},
year={2018}
journal={Science advances},
volume={5},
number={10},
pages={eaav7444},
year={2019},
publisher={American Association for the Advancement of Science}
}
@Article{Goerg2019,
......@@ -515,10 +519,14 @@ pages = {639}
@article{schweizer2019,
title={Floquet approach to $\mathbb{Z}_2$ lattice gauge theories with ultracold atoms in optical lattices},
title={Floquet approach to ℤ 2 lattice gauge theories with ultracold atoms in optical lattices},
author={Schweizer, Christian and Grusdt, Fabian and Berngruber, Moritz and Barbiero, Luca and Demler, Eugene and Goldman, Nathan and Bloch, Immanuel and Aidelsburger, Monika},
journal={arXiv preprint arXiv:1901.07103},
year={2019}
journal={Nature Physics},
volume={15},
number={11},
pages={1168--1173},
year={2019},
publisher={Nature Publishing Group}
}
@article{Klumper2002,
......@@ -2153,13 +2161,6 @@ url={https://doi.org/10.1038/nphys2750}
}
@article{Verstraete2004,
title={Renormalization algorithms for quantum-many body systems in two and higher dimensions},
author={Verstraete, Frank and Cirac, J Ignacio},
journal={arXiv preprint cond-mat/0407066},
year={2004}
}
@article{Verstraete2004b,
title={Matrix product density operators: simulation of finite-temperature and dissipative systems},
author={Verstraete, Frank and Garcia-Ripoll, Juan J and Cirac, Juan Ignacio},
......@@ -3593,12 +3594,15 @@ title= {More is different}
@article{Genkina2018,
title={Imaging topology of Hofstadter ribbons},
author={Genkina, Dina and Aycock, Lauren M and Lu, Hsin-I and Pineiro, Alina M and Lu, Mingwu and Spielman, IB},
journal={arXiv preprint arXiv:1804.06345},
year={2018}
author={Genkina, Dina and Aycock, Lauren M and Lu, Hsin-I and Lu, Mingwu and Pineiro, Alina M and Spielman, IB},
journal={New Journal of Physics},
volume={21},
number={5},
pages={053021},
year={2019},
publisher={IOP Publishing}
}
@book{chien1980hall,
title={The Hall effect and its applications},
editor={Chien, C and C. Westgate},
......@@ -4961,20 +4965,6 @@ year = {1883},
publisher={Nature Publishing Group}
}
@article{Guo2019,
title={Supersolid and pair correlations of extended Jaynes-Cummings-Hubbard model on the triangular and one dimensional lattices},
author={Guo, Lijuan and Greschner, Sebastian and Zhu, Siyu and Zhang, Wanzhou},
journal={arXiv preprint arXiv:1611.06404},
year={2016}
}
@article{rubio2018probing,
title={Probing many-body localization in the presence of a quantum bath},
author={Rubio-Abadal, Antonio and Choi, Jae-yoon and Zeiher, Johannes and Hollerith, Simon and Rui, Jun and Bloch, Immanuel and Gross, Christian},
journal={arXiv preprint arXiv:1805.00056},
year={2018}
}
@article{salomon2019direct,
title={Direct observation of incommensurate magnetism in Hubbard chains},
author={Salomon, Guillaume and Koepsell, Joannis and Vijayan, Jayadev and Hilker, Timon A and Nespolo, Jacopo and Pollet, Lode and Bloch, Immanuel and Gross, Christian},
......
......@@ -27,7 +27,7 @@ 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, and "suitable for
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.
\vspace{2mm}
......@@ -48,6 +48,27 @@ L. Cardarelli, S. Greschner and L. Santos
%------------------------------------------%
%------------------------------------------%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% REFEREE A
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\noindent\makebox[\linewidth]{\rule{\textwidth}{1pt}}
List of changes
\noindent\makebox[\linewidth]{\rule{\textwidth}{1pt}}
\begin{itemize}
\item extended discussion of the 2-leg ladder model and analogies and differences to the present paper in the SM
\item updated Fig.1a
\item new section ``Relation to quantum dimer models'' in the SM
\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 several corrected typos, updated references
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% REFEREE A
......
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\@writefile{toc}{\contentsline {title}{Supplementary material to "Deconfining disordered phase in two-dimensional quantum link models"}{1}{}}
......@@ -13,24 +13,30 @@
\newlabel{eq:lgt1dMPS}{{3}{1}{}{}{}}
\citation{pollmann2012symmetry}
\citation{Cardarelli2017}
\citation{Cardarelli2017}
\citation{Pollmann2010,Pollmann2012,Pollmann2012A}
\@writefile{lof}{\contentsline {figure}{\numberline {S2}{\ignorespaces Mid-system entanglement spectrum of the QLM Eq.\nobreakspace {}(1) of the main text at $\mu =0$ for (a) two-leg ladder, $L=200$ (b) three-leg ladder, $L=100$ (c) four-leg ladder, $L=100$ (DMRG data).}}{2}{}}
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\@writefile{toc}{\contentsline {section}{\numberline {IV}Two-leg cylinder}{2}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {S5}{\ignorespaces Comparison of charge and spin configurations obtained from DMRG results for the intermediate phase ($J_x=J_y$, $\mu =0$) (plots (a),(c), and (e)) to the RK state obtained by an equal amplitude overlap of all connected configurations (plots (b), (d), and (f)) for the four-leg cylinder (a) and (b), the four-leg ladder (c) and (d), and the three-leg ladder (e) and (f)}}{3}{}}
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\bibcite{Shastry1981}{{1}{1981}{{Shastry\ and\ Sutherland}}{{}}}
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\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}{}}
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\bibcite{Ralko2005}{{4}{2005}{{Ralko\ \emph {et~al.}}}{{Ralko, Ferrero, Becca, Ivanov,\ and\ Mila}}}
......@@ -44,17 +50,12 @@
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