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  1. We consider a SU(2) lattice gauge theory on the square lattice, with a single fundamental complex fermion and a single fundamental complex boson on each lattice site. Projective symmetries of the gauge-charged fermions are chosen so that they match with those of the spinons of theπ-flux spin liquid. Global symmetries of all gauge-invariant observables are chosen to match with those of the particle-hole symmetric electronic Hubbard model at half-filling. Consequently, both the fundamental fermion and fundamental boson move in an average backgroundπ-flux, their gauge-invariant composite is the physical electron, and eliminating gauge fields in a strong gauge-coupling expansion yields an effective extended Hubbard model for the electrons. The SU(2) gauge theory displays several confining/Higgs phases: a nodald-wave superconductor, and states with Néel, valence-bond solid, charge, or staggered current orders. There are also a number of quantum phase transitions between these phases that are very likely described by(2+1)-dimensional deconfined conformal gauge theories, and we present large flavor expansions for such theories. These include the phenomenologically attractive case of a transition between a conventional insulator with a charge gap and Néel order, and a conventionald-wave superconductor with gapless Bogoliubov quasiparticles at four nodal points in the Brillouin zone. We also apply our approach to the honeycomb lattice, where we find a bicritical point at the junction of Néel, valence bond solid (Kekulé), and Dirac semimetal phases.

    <supplementary-material><permissions><copyright-statement>Published by the American Physical Society</copyright-statement><copyright-year>2024</copyright-year></permissions></supplementary-material></sec> </div> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> <div class="actions" style="padding-left:10px;"> <span class="reader-count"> Free, publicly-accessible full text available July 1, 2025</span> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10482021-model-wave-superconductivity-antiferromagnetism-charge-order-square-lattice" itemprop="url"> <span class='span-link' itemprop="name">A model of d -wave superconductivity, antiferromagnetism, and charge order on the square lattice</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1073/pnas.2302701120" target="_blank" title="Link to document DOI">https://doi.org/10.1073/pnas.2302701120  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Christos, Maine</span> <span class="sep">; </span><span class="author" itemprop="author">Luo, Zhu-Xi</span> <span class="sep">; </span><span class="author" itemprop="author">Shackleton, Henry</span> <span class="sep">; </span><span class="author" itemprop="author">Zhang, Ya-Hui</span> <span class="sep">; </span><span class="author" itemprop="author">Scheurer, Mathias S.</span> <span class="sep">; </span><span class="author" itemprop="author">Sachdev, Subir</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2023-05-23">May 2023</time> , Proceedings of the National Academy of Sciences) </span> </div> <div style="cursor: pointer;-webkit-line-clamp: 5;" class="abstract" itemprop="description"> <p>We describe the confining instabilities of a proposed quantum spin liquid underlying the pseudogap metal state of the hole-doped cuprates. The spin liquid can be described by a SU(2) gauge theory of<italic>N</italic><sub><italic>f</italic></sub>= 2 massless Dirac fermions carrying fundamental gauge charges—this is the low-energy theory of a mean-field state of fermionic spinons moving on the square lattice with<italic>π</italic>-flux per plaquette in the ℤ<sub>2</sub>center of SU(2). This theory has an emergent SO(5)<sub><italic>f</italic></sub>global symmetry and is presumed to confine at low energies to the Néel state. At nonzero doping (or smaller Hubbard repulsion<italic>U</italic>at half-filling), we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges also moving in<italic>π</italic>ℤ<sub>2</sub>-flux. At half-filling, the low-energy theory of the Higgs sector has<italic>N</italic><sub><italic>b</italic></sub>= 2 relativistic bosons with a possible emergent SO(5)<sub><italic>b</italic></sub>global symmetry describing rotations between a<italic>d</italic>-wave superconductor, period-2 charge stripes, and the time-reversal breaking “<italic>d</italic>-density wave” state. We propose a conformal SU(2) gauge theory with<italic>N</italic><sub><italic>f</italic></sub>= 2 fundamental fermions,<italic>N</italic><sub><italic>b</italic></sub>= 2 fundamental bosons, and a SO(5)<sub><italic>f</italic></sub>×SO(5)<sub><italic>b</italic></sub>global symmetry, which describes a deconfined quantum critical point between a confining state which breaks SO(5)<sub><italic>f</italic></sub>and a confining state which breaks SO(5)<sub><italic>b</italic></sub>. The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order and<italic>d</italic>-wave superconductivity. A similar theory applies at nonzero doping and large<italic>U</italic>, with longer-range couplings of the chargons leading to charge order with longer periods.</p> </div> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> <div class="actions" style="padding-left:10px;"> <span class="reader-count"> <a class="misc external-link" href="https://doi.org/10.1073/pnas.2302701120" target="_blank" title="Link to document DOI" data-ostiid="10482021"> Full Text Available <span class="fas fa-external-link-alt"></span> </a> </span> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10421397-twisted-bilayer-dirac-spin-liquids" itemprop="url"> <span class='span-link' itemprop="name">Twisted bilayer U(1) Dirac spin liquids</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevB.106.144437" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevB.106.144437  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Luo, Zhu-Xi</span> <span class="sep">; </span><span class="author" itemprop="author">Seifert, Urban F.</span> <span class="sep">; </span><span class="author" itemprop="author">Balents, Leon</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2022-10-01">October 2022</time> , Physical Review B) </span> </div> <div class="actions" style="padding-left:10px;"> <span class="reader-count"> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevB.106.144437" target="_blank" title="Link to document DOI" data-ostiid="10421397"> Full Text Available <span class="fas fa-external-link-alt"></span> </a> </span> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10382915-interaction-driven-metal-insulator-transition-charge-fractionalization" itemprop="url"> <span class='span-link' itemprop="name">Interaction-Driven Metal-Insulator Transition with Charge Fractionalization</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevX.12.021067" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevX.12.021067  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Xu, Yichen</span> <span class="sep">; </span><span class="author" itemprop="author">Wu, Xiao-Chuan</span> <span class="sep">; </span><span class="author" itemprop="author">Ye, Mengxing</span> <span class="sep">; </span><span class="author" itemprop="author">Luo, Zhu-Xi</span> <span class="sep">; </span><span class="author" itemprop="author">Jian, Chao-Ming</span> <span class="sep">; </span><span class="author" itemprop="author">Xu, Cenke</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2022-06-01">June 2022</time> , Physical Review X) </span> </div> <div class="actions" style="padding-left:10px;"> <span class="reader-count"> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevX.12.021067" target="_blank" title="Link to document DOI" data-ostiid="10382915"> Full Text Available <span class="fas fa-external-link-alt"></span> </a> </span> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10382912-magic-continuum-twisted-bilayer-square-lattice-staggered-flux" itemprop="url"> <span class='span-link' itemprop="name">Magic continuum in a twisted bilayer square lattice with staggered flux</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevB.104.035136" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevB.104.035136  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Luo, Zhu-Xi</span> <span class="sep">; </span><span class="author" itemprop="author">Xu, Cenke</span> <span class="sep">; </span><span class="author" itemprop="author">Jian, Chao-Ming</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2021-07-01">July 2021</time> , Physical Review B) </span> </div> <div class="actions" style="padding-left:10px;"> <span class="reader-count"> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevB.104.035136" target="_blank" title="Link to document DOI" data-ostiid="10382912"> Full Text Available <span class="fas fa-external-link-alt"></span> </a> </span> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10049906-spinon-magnetic-resonance-quantum-spin-liquids" itemprop="url"> <span class='span-link' itemprop="name">Spinon Magnetic Resonance of Quantum Spin Liquids</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevLett.120.037204" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevLett.120.037204  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Luo, Zhu-Xi</span> <span class="sep">; </span><span class="author" itemprop="author">Lake, Ethan</span> <span class="sep">; </span><span class="author" itemprop="author">Mei, Jia-Wei</span> <span class="sep">; </span><span class="author" itemprop="author">Starykh, Oleg A.</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2018-01-01">January 2018</time> , Physical Review Letters) </span> </div> <div class="actions" style="padding-left:10px;"> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10023106-landau-zener-transition-driven-slow-noise" itemprop="url"> <span class='span-link' itemprop="name">Landau-Zener transition driven by slow noise</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevB.95.064305" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevB.95.064305  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Luo, Zhu-Xi</span> <span class="sep">; </span><span class="author" itemprop="author">Raikh, M. E.</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2017-02-01">February 2017</time> , Physical Review B) </span> </div> <div class="actions" style="padding-left:10px;"> </div> </div><div class="clearfix"></div> </div> </li> </ol> <div id="pagination-lower" style="display:none;"> <div class="pull-right" style="line-height: 30px;"> <div class="btn-group pagination nomargin"> <a href="#" class="btn btn-sm btn-default noborderradius" disabled="disabled">«<span class="hidden-xs"> Prev</span></a> <a class="dropdown-toggle btn btn-sm btn-default paging-dropdown disabled hidden-xs noborderradius" href="#" data-toggle="dropdown"> <span class="caret"></span> <span class="sr-only" style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);">Select page number</span> </a> <a href="#" class="btn btn-sm btn-default noborderradius" disabled="disabled"><span class="hidden-xs">Next </span>»</a> </div> </div> <div class="clearfix"></div> </div> </div> </div> </div> <!-- / basic search results --> </div> </div> <input type='hidden' id='schtype' value=''/> </div> </div> <footer class="row" id="footer-wrapper"> <div class="footer-content"> <div id="footerOSTI" class=" hidden-print"> <ul> <li><a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/">Website Policies</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/about/performance/">Budget and Performance</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/oig/">Inspector General</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/privacy.jsp">Privacy</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/foia.jsp">FOIA</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/od/odi/notice.jsp">No FEAR Act</a> | <a target="_blank" rel="noreferrer" href="http://usa.gov">USA.gov</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/access.jsp">Accessibility</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/nsf_plain_language.jsp">Plain Language</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/help/contact.jsp">Contact</a> | <a target="_blank" rel="noreferrer" href="https://nsf.gov/help/">Help</a> </li> </ul> The National Science Foundation, 2415 Eisenhower Avenue, Alexandria, Virginia 22314, USA Tel: (703) 292-5111, FIRS: (800) 877-8339 | TDD: (800) 281-8749 </div> </div> </footer> </div> <div id="authorselect" class="modal" tabindex="-1" role="dialog" aria-labelledby="authorselect_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <div id="authorselect_label">Author Select</div> </div> <form id="authorselect-form" style="margin-bottom: 0px;"> <input type="hidden" name="pg" id="authorselect-pg" value="1" /> <div class="modal-body" id="authorselect_body"> <div class="row"> <div class="col-md-4"> <label for="authorselect-lname">Last Name:</label><br /> <input type="text" name="lname" class="input-sm form-control" id="authorselect-lname" placeholder="Last name" /><br /> </div> <div class="col-md-4"> <label for="authorselect-fname">First Name:</label><br /> <input type="text" name="fname" class="input-sm form-control" id="authorselect-fname" placeholder="First name" /> </div> <div class="col-md-2">  <br /> <a href="#" onclick="$('#authorselect-form').submit(); return false;" class="btn btn-sm btn-default"><span class="fa fa-search"></span><span class="sr-only">Search</span></a> </div> </div> <div class="push_top"></div> <div class="row"> <div class="col-md-12"> <ul class="nav nav-tabs"> <li class="active"><a href="#authorselect-tab-res" id="authorselect-tab-res-btn" data-toggle="tab">Search Results</a></li> <li><a href="#authorselect-tab-sel" id="authorselect-tab-sel-btn" data-toggle="tab">Selected Authors</a></li> </ul> <div class="tab-content"> <div class="tab-pane active" id="authorselect-tab-res" style="max-height: 450px;"> <div class="padding text-muted" id="authorselect-tab-res-content">Type in a name, or the first few letters of a name, in one or both of appropriate search boxes above and select the search button. 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