Commit 50e6482a authored by Sebastian Greschner's avatar Sebastian Greschner

modified: lgt2_paper.aux

	modified:   lgt2_paper.log
	modified:   lgt2_paper.pdf
	modified:   lgt2_paper.tex
parent 4032dda1
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\citation{Wilson1974}
\citation{Kogut1983,Levin2005,Wiese2013}
\citation{Cirac2010,Zohar2011,Kapit2011,Zohar2012,Banerjee2012,Zohar2013,Banerjee2013,Zohar2013b,Tagliacozzo2013,Cardarelli2017,barbiero2018}
\citation{Cirac2010,Zohar2011,Kapit2011,Zohar2012,Banerjee2012,Zohar2013,Banerjee2013,Zohar2013b,Tagliacozzo2013,Stannigel2014,Kasper2016,Cardarelli2017,Zache2018,barbiero2018}
\citation{Martinez2016}
\citation{Bernien2017}
\citation{Clark2018,Goerg2019,schweizer2019}
......@@ -13,34 +13,41 @@
\citation{Shastry1981,Anderson1987,Moessner2002,Ralko2005}
\citation{Bernien2017,Brenes2018,feldmeier2019emergent}
\citation{turner2018scars}
\citation{Banerjee2012,Zohar2012,Banerjee2013,Stannigel2014,Kasper2016,Zache2018,Mil2019}
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\@writefile{toc}{\contentsline {title}{Deconfinement transition and boundary Haldane order in multileg quantum link ladders}{1}{}}
\@writefile{toc}{\contentsline {title}{Deconfining disordered phase in two-dimensional quantum link models}{1}{}}
\@writefile{toc}{\contentsline {abstract}{Abstract}{1}{}}
\newlabel{eq:QLM}{{1}{1}{}{}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces (a) Sketch of the QLM model on a ladder (gray spins depict staggered boundary) or on a torus (associating opposite gray spins). (b-f) Sketches of the quantum phases discussed in this phases: For $\mu =0.8$ striped phases (b) Sy $J_y=2.4 J_x$ (c) Sx, $J_y=0.2 J_x$, for $\mu =-0.8$ vortex-antivortex (Ne\'el) phases (d) VA, $J_y=2.4 J_x$ (e) VA', $J_y=0.2 J_x$ and the (f) disordered/deconfined phase DP for $\mu =0$, $J_x=J_y$. Size of bullets depicts $\delimiter "426830A n_{\mathbf {r}}\delimiter "526930B $, arrow-size $\delimiter "426830A S_{\mathbf {r},\mathbf {r'}}^z\delimiter "526930B $ and plaquette-colors the vorticity $\delimiter "426830A Q_{\mathbf {r}}\delimiter "526930B $, with $Q_{\mathbf {r}} = R_{\mathbf {r}}^+ R_{\mathbf {r}}^- - R_{\mathbf {r}}^- R_{\mathbf {r}}^+$. Arrow sizes of (f) has been scaled by a factor of 2 for clarity.}}{1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces (a) Sketch of the QLM model on a square ladder\nobreakspace {}(gray spins depict staggered boundary conditions) or on a torus (associating opposite gray spins at the two edges). (b-f) Sketches of the phases discussed in the text: for $\mu =0.8$ striped phases (b) $J_y=2.4 J_x$\nobreakspace {}(Sy), (c) $J_y=0.2 J_x$\nobreakspace {}(Sx); for $\mu =-0.8$ vortex-antivortex phases (d) $J_y=2.4 J_x$\nobreakspace {}(VA) (e) $J_y=0.2 J_x$\nobreakspace {}(VA$'$), and the (f) disordered/deconfined D phase for $\mu =0$ and $J_x=J_y$. The size of the bullets depicts $\delimiter "426830A n_{\mathbf {r}}\delimiter "526930B $, the arrow size $\delimiter "426830A S_{\mathbf {r},\mathbf {r'}}^z\delimiter "526930B $, and the plaquette colors the vorticity $\delimiter "426830A Q_{\mathbf {r}}\delimiter "526930B $. The arrow sizes of (f) has been scaled up by a factor of $2$ for clarity.}}{1}{}}
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\@writefile{toc}{\contentsline {paragraph}{\numberline {}2D QLM.--}{1}{}}
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\citation{Schollwock2011}
\citation{Dalmonte2016cont,Tschirsich2019,Chepiga2019dmrg,DMRGnote}
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces 4-leg cylinder at $\mu =0$ (a) Fidelity susceptibility with $L=12$, $24$ and $36$ rungs. (b) Nearest and next-nearest neighbor flippability correlations for the 4-leg cylinder. (c) Sketched phase diagram of the QLM. Color codes depict the von-Neumann bipartite entanglement entropy $S_{vN}$ for the 4-leg ladder in the center of the system. Points depicts the estimated phase transition points for the 4-leg cylinder, by extrapolating the peak positions of the fidelity susceptibility evaluated along the cuts indicated by the dotted lines. (d) Local Hilbert space distribution $\nu _k$ of representative eigenstates of the 4-leg cylinder for the central rung.}}{2}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Four-leg cylinder at $\mu =0$ (a) Fidelity susceptibility with $L=12$, $24$ and $36$ rungs. (b) Nearest and next-nearest neighbor flippability correlations. (c) Sketched phase diagram of the QLM. Color codes depict the von-Neumann bipartite entanglement entropy $S_{vN}$ of the central rung. Points depicts the estimated phase transition points, by extrapolating the peak positions of the fidelity susceptibility evaluated along the cuts indicated by the dotted lines. (d) Local Hilbert space distribution $\nu _k$ of the central rung\nobreakspace {}(see text).}}{2}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces (a) Boundary-parity and string order of Model\nobreakspace {}\textup {\hbox {\mathsurround \z@ \normalfont (\ignorespaces 1{}{}{}\hbox {}\unskip \@@italiccorr )}} on a 4-leg ladder and (b) entanglement spectrum $\lambda _k$, which is the ordered sequence of Schmidt eigenvalues obtained for dividing the system into two parts along the central rung. DMRG data, $\mu =0$, $L=100$.}}{3}{}}
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\citation{Tschirsich2019}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces (a) Charge and bond average configurations of two defects with distance $L_D=12$ sites. DMRG-data, $L=36$ rungs, $\mu =0.4 J_x$ after substracting background without charges. (a) Sy phase ($J_y=1.8 J_x$), (b) Sx ($J_y=0.4 J_x$), (c) DP $J_y=J_x$. (d) String tension $S_T$ as function of the distance between the defects $L_D$.}}{4}{}}
\newlabel{fig:config_4T_ST}{{4}{4}{}{}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces (a) Parity and string order along the boundary legs of a four-leg ladder, obtained using DMRG for $L_x=100$ rungs and $\mu =0$; (b) largest eigenvalues of the entanglement spectrum, obtained after dividing the system into two parts along the central rung.}}{3}{}}
\newlabel{fig:entanglement_SO}{{3}{3}{}{}{}}
\@writefile{toc}{\contentsline {paragraph}{\numberline {}Edge Haldane order.--}{3}{}}
\newlabel{eq:QLM1D}{{2}{3}{}{}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces (a) Average fermionic density and bond configuration of two charges at a distance of $L_D=12$ sites, after substracting the charge-free configuration. We employ DMRG for a cylinder with $L_y=4$ legs and $L=36$ rungs and $\mu =0.4 J_x$. (a) Sy phase\nobreakspace {}($J_y=1.8 J_x$), (b) Sx phase\nobreakspace {}($J_y=0.4 J_x$), (c) D phase\nobreakspace {}($J_y=J_x$). (d) String tension $S_T$ as a function of the distance between the defects $L_D$.}}{3}{}}
\newlabel{fig:config_4T_ST}{{4}{3}{}{}{}}
\@writefile{toc}{\contentsline {paragraph}{\numberline {}String tension.--}{3}{}}
\citation{turner2018scars,feldmeier2019emergent}
\bibdata{lgt2_paperNotes,references}
\bibcite{Wilson1974}{{1}{1974}{{Wilson}}{{}}}
......@@ -65,6 +72,9 @@
\bibcite{schweizer2019}{{20}{2019}{{Schweizer\ \emph {et~al.}}}{{Schweizer, Grusdt, Berngruber, Barbiero, Demler, Goldman, Bloch,\ and\ Aidelsburger}}}
\bibcite{Mil2019}{{21}{2019}{{Mil\ \emph {et~al.}}}{{Mil, Zache, Hegde, Xia, Bhatt, Oberthaler, Hauke, Berges,\ and\ Jendrzejewski}}}
\bibcite{Chandrasekharan1997}{{22}{1997}{{Chandrasekharan\ and\ Wiese}}{{}}}
\@writefile{toc}{\contentsline {paragraph}{\numberline {}Conclusions.--}{4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {}Acknowledgments}{4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {}References}{4}{}}
\bibcite{dai2017four}{{23}{2017}{{Dai\ \emph {et~al.}}}{{Dai, Yang, Reingruber, Sun, Xu, Chen, Yuan,\ and\ Pan}}}
\bibcite{Celi2019}{{24}{2019}{{Celi\ \emph {et~al.}}}{{Celi, Vermersch, Viyuela, Pichler, Lukin,\ and\ Zoller}}}
\bibcite{Bohrdt2019}{{25}{2019}{{Bohrdt\ \emph {et~al.}}}{{Bohrdt, Omran, Demler, Gazit,\ and\ Grusdt}}}
......@@ -88,7 +98,5 @@
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