We analyze a Higgs transition from a U(1) Dirac spin liquid to a gapless ℤ_{2}spin liquid. This ℤ_{2}spin liquid is of relevance to the spin
We describe the confining instabilities of a proposed quantum spin liquid underlying the pseudogap metal state of the holedoped cuprates. The spin liquid can be described by a SU(2) gauge theory of
 Award ID(s):
 2002850
 NSFPAR ID:
 10482021
 Publisher / Repository:
 National Academy of Science
 Date Published:
 Journal Name:
 Proceedings of the National Academy of Sciences
 Volume:
 120
 Issue:
 21
 ISSN:
 00278424
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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A<sc>bstract</sc> S = 1/ 2 square lattice antiferromagnet, where recent numerical studies have given evidence for such a phase existing in the regime of high frustration between nearest neighbor and nextnearest neighbor antiferromagnetic interactions (theJ _{1}J _{2}model), appearing in a parameter regime between the vanishing of Néel order and the onset of valence bond solid ordering. The proximate Dirac spin liquid is unstable to monopole proliferation on the square lattice, ultimately leading to Néel or valence bond solid ordering. As such, we conjecture that this Higgs transition describes the critical theory separating the gapless ℤ_{2}spin liquid of theJ _{1}J _{2}model from one of the two proximate ordered phases. The transition into the other ordered phase can be described in a unified manner via a transition into an unstable SU(2) spin liquid, which we have analyzed in prior work. By studying the deconfined critical theory separating the U(1) Dirac spin liquid from the gapless ℤ_{2}spin liquid in a 1/N _{f}expansion, withN _{f}proportional to the number of fermions, we find a stable fixed point with an anisotropic spinon dispersion and a dynamical critical exponentz ≠ 1. We analyze the consequences of this anisotropic dispersion by calculating the angular profiles of the equaltime Néel and valence bond solid correlation functions, and we find them to be distinct. We also note the influence of the anisotropy on the scaling dimension of monopoles. 
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 gaugecharged fermions are chosen so that they match with those of the spinons of the$\pi $flux spin liquid. Global symmetries of all gaugeinvariant observables are chosen to match with those of the particlehole symmetric electronic Hubbard model at halffilling. Consequently, both the fundamental fermion and fundamental boson move in an average background$\pi $flux, their gaugeinvariant composite is the physical electron, and eliminating gauge fields in a strong gaugecoupling expansion yields an effective extended Hubbard model for the electrons. The SU(2) gauge theory displays several confining/Higgs phases: a nodal$d$wave superconductor, and states with Néel, valencebond solid, charge, or staggered current orders. There are also a number of quantum phase transitions between these phases that are very likely described by$(2+1)$dimensional deconfined conformal gauge theories, and we present large flavor expansions for such theories. These include the phenomenologically attractive case of a transition between a conventional insulator with a charge gap and Néel order, and a conventional$d$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.
<supplementarymaterial><permissions><copyrightstatement>Published by the American Physical Society</copyrightstatement><copyrightyear>2024</copyrightyear></permissions></supplementarymaterial></sec> </div> <a href='#' class='show openabstract' style='marginleft:10px;'>more »</a> <a href='#' class='hide closeabstract' style='marginleft:10px;'>« less</a> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="iteminfo"> <div class="title"> <a href="https://par.nsf.gov/biblio/10434481electroweakflavourunification" itemprop="url"> <span class='spanlink' itemprop="name">Electroweak flavour unification</span> </a> </div> <div> <strong> <a class="misc externallink" href="https://doi.org/10.1007/JHEP09(2022)193" target="_blank" title="Link to document DOI">https://doi.org/10.1007/JHEP09(2022)193 <span class="fas faexternallinkalt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Davighi, Joe</span> <span class="sep">; </span><span class="author" itemprop="author">ToobySmith, Joseph</span> </span> <span class="year">( <time itemprop="datePublished" datetime="20220901">September 2022</time> , Journal of High Energy Physics) </span> </div> <div style="cursor: pointer;webkitlineclamp: 5;" class="abstract" itemprop="description"> A bstract We propose that the electroweak and flavour quantum numbers of the Standard Model (SM) could be unified at high energies in an SU(4) × Sp(6) L × Sp(6) R anomalyfree gauge model. All the SM fermions are packaged into two fundamental fields, Ψ L ∼ ( 4 , 6 , 1 ) and Ψ R ∼ ( 4 , 1 , 6 ), thereby explaining the origin of three families of fermions. The SM Higgs, being electroweakly charged, necessarily becomes charged also under flavour when embedded in the UV model. It is therefore natural for its vacuum expectation value to couple only to the third family. The other components of the UV Higgs fields are presumed heavy. Extra scalars are needed to break this symmetry down to the SM, which can proceed via ‘flavourdeconstructed’ gauge groups; for instance, we propose a pattern Sp(6) L → $$ {\prod}_{i=1}^3\mathrm{SU}{(2)}_{L,i}\to \mathrm{SU}{(2)}_L $$ ∏ i = 1 3 SU 2 L , i → SU 2 L for the lefthanded factor. When the heavy Higgs components are integrated out, realistic quark Yukawa couplings with inbuilt hierarchies are naturally generated without any further ingredients, if we assume the various symmetry breaking scalars condense at different scales. The CKM matrix that we compute is not a generic unitary matrix, but it can precisely fit the observed values. </div> <a href='#' class='show openabstract' style='marginleft:10px;'>more »</a> <a href='#' class='hide closeabstract' style='marginleft:10px;'>« less</a> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="iteminfo"> <div class="title"> <a href="https://par.nsf.gov/biblio/10438924codimensiondefectshighersymmetriestopologicalphases" itemprop="url"> <span class='spanlink' itemprop="name">Codimension2 defects and higher symmetries in (3+1)D topological phases</span> </a> </div> <div> <strong> <a class="misc externallink" href="https://doi.org/10.21468/SciPostPhys.14.4.065" target="_blank" title="Link to document DOI">https://doi.org/10.21468/SciPostPhys.14.4.065 <span class="fas faexternallinkalt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Barkeshli, Maissam</span> <span class="sep">; </span><span class="author" itemprop="author">Chen, YuAn</span> <span class="sep">; </span><span class="author" itemprop="author">Huang, ShengJie</span> <span class="sep">; </span><span class="author" itemprop="author">Kobayashi, Ryohei</span> <span class="sep">; </span><span class="author" itemprop="author">Tantivasadakarn, Nathanan</span> <span class="sep">; </span><span class="author" itemprop="author">Zhu, Guanyu</span> </span> <span class="year">( <time itemprop="datePublished" datetime="20230101">January 2023</time> , SciPost Physics) </span> </div> <div style="cursor: pointer;webkitlineclamp: 5;" class="abstract" itemprop="description"> (3+1)D topological phases of matter can host a broad class of nontrivial topological defects of codimension1, 2, and 3, of which the wellknown point charges and flux loops are special cases. The complete algebraic structure of these defects defines a higher category, and can be viewed as an emergent higher symmetry. This plays a crucial role both in the classification of phases of matter and the possible faulttolerant logical operations in topological quantum errorcorrecting codes. In this paper, we study several examples of such higher codimension defects from distinct perspectives. We mainly study a class of invertible codimension2 topological defects, which we refer to as twist strings. We provide a number of general constructions for twist strings, in terms of gauging lower dimensional invertible phases, layer constructions, and condensation defects. We study some special examples in the context of \mathbb{Z}_2 ℤ 2 gauge theory with fermionic charges, in \mathbb{Z}_2 \times \mathbb{Z}_2 ℤ 2 × ℤ 2 gauge theory with bosonic charges, and also in nonAbelian discrete gauge theories based on dihedral ( D_n D n ) and alternating ( A_6 A 6 ) groups. The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an H^4 H 4 cohomology class that characterizes part of an underlying 3group symmetry of the topological order. The equations involving background gauge fields for the 3group symmetry have been explicitly written down for various cases. We also study examples of twist strings interacting with nonAbelian flux loops (defining part of a noninvertible higher symmetry), examples of noninvertible codimension2 defects, and examples of the interplay of codimension2 defects with codimension1 defects. 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l _{b}−s )2πT , wherel _{b}is the highest integer spin in the theory ands takes all positive integer values. We revisit this formalism in theories with gauge symmetry and upgrade the poleskipping condition so that it works without having to remove the gauge redundancy. We also extend the formalism by incorporating fermions with general spins and interactions and show that their presence generally leads to a separate tower of poleskipping points at frequencies i(l _{f}−s )2πT ,l _{f}being the highest halfinteger spin in the theory ands again taking all positive integer values. We also demonstrate the practical value of this formalism using a selection of examples with spins 0, $$ \frac{1}{2} $$ $\frac{1}{2}$, 1, $$ \frac{3}{2} $$ $\frac{3}{2}$, 2.