Symmetry group
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Fermion path integrals and topological phases Open
Symmetry-protected topological (SPT) phases of matter have been interpreted in terms of anomalies, and it has been expected that a similar picture should hold for SPT phases with fermions. Here, we describe in detail what this picture mean…
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Symmetry-Based Computational Tools for Magnetic Crystallography Open
In recent years, two important advances have opened new doors for the characterization and determination of magnetic structures. Firstly, researchers have produced computer-readable listings of the magnetic or Shubnikov space groups. Secon…
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Flat space amplitudes and conformal symmetry of the celestial sphere Open
The four-dimensional (4D) Lorentz group $SL(2,\\mathbb{C})$ acts as the\ntwo-dimensional (2D) global conformal group on the celestial sphere at infinity\nwhere asymptotic 4D scattering states are specified. Consequent similarities of\n4D f…
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On 2-group global symmetries and their anomalies Open
In general quantum field theories (QFTs), ordinary (0-form) global symmetries and 1-form symmetries can combine into 2-group global symmetries. We describe this phenomenon in detail using the language of symmetry defects. We exhibit a simp…
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Double crystallographic groups and their representations on the Bilbao Crystallographic Server Open
A new section of databases and programs devoted to double crystallographic groups (point and space groups) has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The double crystallographic groups are require…
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Classification of topological phases in periodically driven interacting systems Open
We consider topological phases in periodically driven (Floquet) systems\nexhibiting many-body localization, protected by a symmetry $G$. We argue for a\ngeneral correspondence between such phases and topological phases of undriven\nsystems…
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Field-Theory Representation of Gauge-Gravity Symmetry-Protected Topological Invariants, Group Cohomology, and Beyond Open
The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landa…
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Topological Phases Protected by Point Group Symmetry Open
We consider symmetry protected topological (SPT) phases with crystalline\npoint group symmetry, dubbed point group SPT (pgSPT) phases. We show that such\nphases can be understood in terms of lower-dimensional topological phases with\non-si…
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Notes on generalized global symmetries in QFT Open
It was recently argued that quantum field theories possess one‐form and higher‐form symmetries, labelled ‘generalized global symmetries.’ In this paper, we describe how those higher‐form symmetries can be understood mathematically as speci…
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Spin-Group Symmetry in Magnetic Materials with Negligible Spin-Orbit Coupling Open
Symmetry formulated by group theory plays an essential role with respect to\nthe laws of nature, from fundamental particles to condensed matter systems.\nHere, by combining symmetry analysis and tight-binding model calculations, we\nelucid…
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Universal Non‐Invertible Symmetries Open
It is well‐known that gauging a finite 0‐form symmetry in a quantum field theory leads to a dual symmetry generated by topological Wilson line defects. These are described by the representations of the 0‐form symmetry group which form a 1‐…
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Group-Invariant Quantum Machine Learning Open
Quantum machine learning (QML) models are aimed at learning from data encoded in quantum states. Recently, it has been shown that models with little to no inductive biases (i.e., with no assumptions about the problem embedded in the model)…
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Three-body spectrum in a finite volume: The role of cubic symmetry Open
The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the BetheSalpeter equation for particle-dime…
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Higher form symmetries and M-theory Open
We discuss the geometric origin of discrete higher form symmetries of quantum field theories in terms of defect groups from geometric engineering in M-theory. The flux non-commutativity in M-theory gives rise to (mixed) ’t Hooft anomalies …
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Symmetry-enriched string nets: Exactly solvable models for SET phases Open
We construct exactly solvable models for a wide class of symmetry enriched topological (SET) phases. Our construction applies to 2D bosonic SET phases with finite unitary onsite symmetry group $G$ and we conjecture that our models realize …
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The Λ-BMS<sub>4</sub> group of dS<sub>4</sub> and new boundary conditions for AdS<sub>4</sub> Open
Using the dictionary between Bondi and Fefferman-Graham gauges, we identify the analogues of the Bondi news, Bondi mass and Bondi angular momentum aspects at the boundary of generic asymptotically locally (A)dS4 spacetimes. We introduce th…
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Asymptotic density of states in 2d CFTs with non-invertible symmetries Open
A bstract It is known that the asymptotic density of states of a 2d CFT in an irreducible representation ρ of a finite symmetry group G is proportional to (dim ρ ) 2 . We show how this statement can be generalized when the symmetry can be …
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A third-order nonlinear Schrödinger equation: the exact solutions, group-invariant solutions and conservation laws Open
In this study, we consider the third order nonlinear Schrödinger equation (TONSE) that models the wave pulse transmission in a time period less than one-trillionth of a second. With the help of the extended modified method, we obtain numer…
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Composite Weyl nodes stabilized by screw symmetry with and without time-reversal invariance Open
We classify the band degeneracies in three-dimensional crystals with screw symmetry nm and broken P∗T symmetry, where P stands for spatial inversion and T for time reversal. The generic degeneracies along symmetry lines are Weyl nodes: chi…
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Topological invariants for gauge theories and symmetry-protected topological phases Open
We study the braiding statistics of particle-like and loop-like excitations in 2D and 3D gauge theories with finite, Abelian gauge group. The gauge theories that we consider are obtained by gauging the symmetry of gapped, short-range entan…
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Projective symmetry group classification of chiral spin liquids Open
We present a general review of the projective symmetry group classification\nof fermionic quantum spin liquids for lattice models of spin $S=1/2$. We then\nintroduce a systematic generalization of the approach for symmetric\n$\\mathbb{Z}_2…
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BMS supertranslations and memory in four and higher dimensions Open
We consider the memory effect in even dimensional spacetimes of dimension $d\n\\ge 4$ arising from a burst of gravitational radiation. When $d=4$, the natural\nframes in the stationary eras before and after the burst differ by the\ncomposi…
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Modular flavor symmetry on a magnetized torus Open
We study the modular invariance in magnetized torus models. Modular invariant\nflavor model is a recently proposed hypothesis for solving the flavor puzzle,\nwhere the flavor symmetry originates from modular invariance. In this framework\n…
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Enumeration and Representation Theory of Spin Space Groups Open
Fundamental physical properties, such as phase transitions, electronic structures, and spin excitations, in all magnetic ordered materials, were ultimately believed to rely on the symmetry theory of magnetic space groups. Recently, it has …
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On continuous 2-category symmetries and Yang-Mills theory Open
A bstract We study a 4d gauge theory U(1) N− 1 ⋊ S N obtained from a U(1) N− 1 theory by gauging a 0-form symmetry S N . We show that this theory has a global continuous 2-category symmetry, whose structure is particularly rich for N > 2. …
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Computational Power of Symmetry-Protected Topological Phases Open
We consider ground states of quantum spin chains with symmetry-protected topological (SPT) order as resources for measurement-based quantum computation (MBQC). We show that, for a wide range of SPT phases, the computational power of ground…
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2-Group symmetries and their classification in 6d Open
We uncover 2-group symmetries in 6d superconformal field theories. These symmetries arise when the discrete 1-form symmetry and continuous flavor symmetry group of a theory mix with each other. We classify all 6d superconformal field theor…
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Quasisymmetry Groups and Many-Body Scar Dynamics Open
In quantum systems, a subspace spanned by degenerate eigenvectors of the Hamiltonian may have higher symmetries than those of the Hamiltonian itself. When this enhanced-symmetry group can be generated from local operators, we call it a qua…
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Many-body topological invariants in fermionic symmetry-protected topological phases: Cases of point group symmetries Open
We propose the definitions of many-body topological invariants to detect\nsymmetry-protected topological phases protected by point group symmetry, using\npartial point group transformations on a given short-range entangled quantum\nground …
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Eliminating fermionic matter fields in lattice gauge theories Open
We devise a unitary transformation that replaces the fermionic degrees of\nfreedom of lattice gauge theories by (hard-core) bosonic ones. The resulting\ntheory is local and gauge invariant, with the same symmetry group. The method\nworks i…