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1. Entanglement-enabled symmetry-breaking orders

   https://doi.org/10.21468/SciPostPhysCore.7.1.010  

   Lin, Cheng-Ju; Zou, Liujun (January 2024, SciPost Physics Core)

   A spontaneous symmetry-breaking order is conventionally described by a tensor-product wavefunction of some few-body clusters; some standard examples include the simplest ferromagnets and valence bond solids. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any such tensor-product state. Given a symmetry breaking pattern, we propose a criterion to diagnose if the symmetry-breaking order is entanglement-enabled, by examining the compatibility between the symmetries and the tensor-product description. For concreteness, we present an infinite family of exactly solvable gapped models on one-dimensional lattices with nearest-neighbor interactions, whose ground states exhibit entanglement-enabled symmetry-breaking orders from a discrete symmetry breaking. In addition, these ground states have gapless edge modes protected by the unbroken symmetries. We also propose a construction to realize entanglement-enabled symmetry-breaking orders with spontaneously broken continuous symmetries. Under the unbroken symmetries, some of our examples can be viewed as symmetry-protected topological states that are beyond the conventional classifications. 

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2. Spacetime Subsystem Symmetries

   Baig, Saba A; Distler, Jacques; Karch, Andreas; Raz, Amir; Sun, Hao-Yu (March 2023, arXiv)

   One characteristic feature of many fractonic lattice models, and a defining property of the exotic field theories developed to describe them, are subsystem symmetries including a conservation of not just net electric charge but also electric dipole moments or charges living on submanifolds. So far all such theories were based on internal subsystem symmetries. In this work we generalize the notion of subsystem symmetries to system with subsystem spacetime symmetries with locally conserved energies. 

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3. Quantum phases and transitions in spin chains with non-invertible symmetries

   https://doi.org/10.21468/SciPostPhys.17.4.115  

   Chatterjee, Arkya; Aksoy, Ömer Mert; Wen, Xiao-Gang (January 2024, SciPost Physics)

   Generalized symmetries often appear in the form of emergent symmetries in low energy effective descriptions of quantum many-body systems. Non-invertible symmetries are a particularly exotic class of generalized symmetries, in that they are implemented by transformations that do not form a group. Such symmetries appear generically in gapless states of quantum matter constraining the low-energy dynamics. To provide a UV-complete description of such symmetries, it is useful to construct lattice models that respect these symmetries exactly. In this paper, we discuss two families of one-dimensional lattice Hamiltonians with finite on-site Hilbert spaces: one with (invertible) $$S^{\,}_3$$ symmetry and the other with non-invertible $$\mathsf{Rep}(S^{\,}_3)$$ symmetry. Our models are largely analytically tractable and demonstrate all possible spontaneous symmetry breaking patterns of these symmetries. Moreover, we use numerical techniques to study the nature of continuous phase transitions between the different symmetry-breaking gapped phases associated with both symmetries. Both models have self-dual lines, where the models are enriched by (intrinsic) non-invertible symmetries generated by Kramers-Wannier-like duality transformations. We provide explicit lattice operators that generate these non-invertible self-duality symmetries. We show that the enhanced symmetry at the self-dual lines is described by a 2+1D symmetry-topological-order (SymTO) of type $$\overline{\mathrm{JK}}^{\,}_4\times \mathrm{JK}^{\,}_4$$. The condensable algebras of the SymTO determine the allowed gapped and gapless states of the self-dual $$S^{\,}_3$$-symetric and $$\mathsf{Rep}(S^{\,}_3)$$-symmetric models. 

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4. Generalized symmetries of topological field theories

   https://doi.org/10.1007/JHEP03(2023)087  

   Gripaios, Ben; Randal-Williams, Oscar; Tooby-Smith, Joseph (March 2023, Journal of High Energy Physics)

   A bstract We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed is forgotten. Doing so allows many questions of physical interest to be answered using the tools of homotopy theory. We study both global and gauge symmetries, as well as ‘t Hooft anomalies, which we show fall into one of two classes. Our approach also allows some insight into earlier work on symmetries (generalized or not) of topological field theories. 

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5. Singular angular magnetoresistance in a magnetic nodal semimetal

   https://doi.org/10.1126/science.aat0348  

   Suzuki, T.; Savary, L.; Liu, J.-P.; Lynn, J. W.; Balents, L.; Checkelsky, J. G. (July 2019, Science)

   Transport coefficients of correlated electron systems are often useful for mapping hidden phases with distinct symmetries. Here we report a transport signature of spontaneous symmetry breaking in the magnetic Weyl semimetal cerium-aluminum-germanium (CeAlGe) system in the form of singular angular magnetoresistance (SAMR). This angular response exceeding 1000% per radian is confined along the high-symmetry axes with a full width at half maximum reaching less than 1° and is tunable via isoelectronic partial substitution of silicon for germanium. The SAMR phenomena is explained theoretically as a consequence of controllable high-resistance domain walls, arising from the breaking of magnetic point group symmetry strongly coupled to a nearly nodal electronic structure. This study indicates ingredients for engineering magnetic materials with high angular sensitivity by lattice and site symmetries. 

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