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1. Deconfined quantum criticality of nodal $d$ -wave superconductivity, Néel order, and charge order on the square lattice at half-filling

   https://doi.org/10.1103/PhysRevResearch.6.033018  

   Christos, Maine; Shackleton, Henry; Sachdev, Subir; Luo, Zhu-Xi (July 2024, Physical Review Research)

   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 the $\pi$-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 background $\pi$-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 nodal $d$-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 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. Published by the American Physical Society2024 

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2. More about the lattice Hamiltonian for Adjoint QCD2

   https://doi.org/10.1007/JHEP06(2025)260  

   Dempsey, Ross; Pufu, Silviu S; Søgaard, Benjamin T; Klebanov, Igor R (June 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> In our earlier work [1], we introduced a lattice Hamiltonian for Adjoint QCD₂using staggered Majorana fermions. We found the gauge invariant space of states explicitly for the gauge group SU(2) and used them for numerical calculations of observables, such as the spectrum and the expectation value of the fermion bilinear. In this paper, we carry out a more in-depth study of our lattice model, extending it to any compact and simply-connected gauge groupG. We show how to find the gauge invariant space of states and use it to study various observables. We also use the lattice model to calculate the mixed ’t Hooft anomalies of Adjoint QCD₂for arbitraryG. We show that the matrix elements of the lattice Hamiltonian can be expressed in terms of the Wigner 6j-symbols ofG. ForG= SU(3), we perform exact diagonalization for lattices of up to six sites and study the low-lying spectrum, the fermion bilinear condensate, and the string tension. We also show how to write the lattice strong coupling expansion for ground state energies and operator expectation values in terms of the Wigner 6j-symbols. For SU(3) we carry this out explicitly and find good agreement with the exact diagonalizations, and for SU(4) we give expansions that can be compared with future numerical studies. 

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3. Stabilizer Scars

   https://doi.org/10.1103/n5hb-l5p5  

   Hartse, Jeremy; Fidkowski, Lukasz; Mueller, Niklas (August 2025, Physical Review Letters)

   Quantum many-body scars are eigenstates in nonintegrable isolated quantum systems that defy typical thermalization paradigms, violating the eigenstate thermalization hypothesis and quantum ergodicity. We identify exact analytic scar solutions in a 2 + 1 dimensional lattice gauge theory in a quasi-1D limit as zeromagic resource stabilizer states. Our results also highlight the importance of magic resources for gauge theory thermalization, revealing a connection between computational complexity and quantum ergodicity. 

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4. Symmetric states and dynamics of three quantum bits

   https://doi.org/10.26421/QIC22.7-8-1  

   Albertini, Francesca; D'Alessandro, Domenico (May 2022, Quantum Information and Computation)

   The unitary group acting on the Hilbert space $${\cal H}:=(C^2)^{\otimes 3}$$ of three quantum bits admits a Lie subgroup, $$U^{S_3}(8)$$, of elements which permute with the symmetric group of permutations of three objects. Under the action of such a Lie subgroup, the Hilbert space $${\cal H}$$ splits into three invariant subspaces of dimensions $$4$$, $$2$$ and $$2$$ respectively, each corresponding to an irreducible representation of $su(2)$. The subspace of dimension $$4$$ is uniquely determined and corresponds to states that are themselves invariant under the action of the symmetric group. This is the so called {\it symmetric sector.} The subspaces of dimension two are not uniquely determined and we parametrize them all. We provide an analysis of pure states that are in the subspaces invariant under $$U^{S_3}(8)$. This concerns their entanglement properties, separability criteria and dynamics under the Lie subgroup $$U^{S_3}(8)$$. As a physical motivation for the states and dynamics we study, we propose a physical set-up which consists of a symmetric network of three spin $$\frac{1}{2}$$ particles under a common driving electro-magnetic field. {For such system, we solve the control theoretic problem of driving a separable state to a state with maximal distributed entanglement. 

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5. Electroweak flavour unification

   https://doi.org/10.1007/JHEP09(2022)193  

   Davighi, Joe; Tooby-Smith, Joseph (September 2022, Journal of High Energy Physics)

   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 anomaly-free 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 ‘flavour-deconstructed’ 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 left-handed factor. When the heavy Higgs components are integrated out, realistic quark Yukawa couplings with in-built 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. 

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