Invariants for (2+1)D bosonic crystalline topological insulators for all 17 wallpaper groups

• URL: http://arxiv.org/abs/2510.26074v1
• Date: Thu, 30 Oct 2025 02:13:14 GMT
• Title: Invariants for (2+1)D bosonic crystalline topological insulators for all 17 wallpaper groups
• Authors: Vladimir Calvera, Naren Manjunath, Maissam Barkeshli,
• Abstract summary: We study bosonic symmetry-protected topological (SPT) phases in (2+1) dimensions with symmetry $G = G_textspacetimes K$.<n>In each case we propose a set of many-body invariants that can detect all the different phases predicted from real space constructions and group cohomology classifications.<n>We verify our proposal through exact calculations on ground states constructed using real space constructions.
• Score: 4.71547360356314
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study bosonic symmetry-protected topological (SPT) phases in (2+1) dimensions with symmetry $G = G_{\text{space}}\times K$, where $G_{\text{space}}$ is a general wallpaper group and $K=\text{U}(1),\mathbb{Z}_N, \text{SO}(3)$ is an internal symmetry. In each case we propose a set of many-body invariants that can detect all the different phases predicted from real space constructions and group cohomology classifications. They are obtained by applying partial rotations and reflections to a given ground state, combined with suitable operations in $K$. The reflection symmetry invariants that we introduce include `double partial reflections', `weak partial reflections' and their `relative' or `twisted' versions which also depend on $K$. We verify our proposal through exact calculations on ground states constructed using real space constructions. We demonstrate our method in detail for the groups p4m and p4g, and in the case of p4m also derive a topological effective action involving gauge fields for orientation-reversing symmetries. Our results provide a concrete method to fully characterize (2+1)D crystalline topological invariants in bosonic SPT ground states.

Related papers

• A Cohomological Framework for Topological Phases from Momentum-Space Crystallographic Groups [6.212797494435471]
  We show that the cohomological theory of MCGs encodes fundamental data of crystalline topological band structures.<n>The theory serves as a key technical framework for analyzing crystalline topological phases within the general setting of projective symmetry.
  arXiv  Detail & Related papers  (2025-12-26T03:33:24Z)
• Topological nature of edge states for one-dimensional systems without symmetry protection [46.87902365052209]
  We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells)<n>Our winding number is invariant under unitary or similarity transforms.
  arXiv  Detail & Related papers  (2024-12-13T19:44:54Z)
• Domain walls from SPT-sewing [43.87233488320917]
  We propose a correspondence between 1d SPT phases with a non-invertible $Gtimes textRep(G)times G$ symmetry and invertible domain walls in the quantum double associated with the group $G$. We also use our method to construct emphanchoring domain walls, which are novel exotic domain walls in the 3d toric code that transform point-like excitations to semi-loop-like excitations anchored on these domain walls.
  arXiv  Detail & Related papers  (2024-11-18T19:00:16Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Non-invertible symmetry-protected topological order in a group-based cluster state [0.5461938536945721]
  We introduce a one-dimensional stabilizer Hamiltonian composed of group-based Pauli operators whose ground state is a $Gtimes textRep(G)$-symmetric state.<n>We show that this state lies in a symmetry-protected topological (SPT) phase protected by $Gtimes textRep(G)$ symmetry, distinct from the symmetric product state by a duality argument.
  arXiv  Detail & Related papers  (2023-12-14T18:56:20Z)
• Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups [0.0]
  We develop a characterization and classification of interacting, invertible fermionic topological phases in (2+1) dimensions. We derive a topological response theory in terms of background crystalline gauge fields. We derive an explicit map between the free and interacting classifications.
  arXiv  Detail & Related papers  (2023-09-21T18:00:01Z)
• Complete crystalline topological invariants from partial rotations in (2+1)D invertible fermionic states and Hofstadter's butterfly [6.846670002217106]
  We show how to extract many-body invariants $Theta_textopm$, where $texto$ is a high symmetry point, from partial rotations in (2+1)D invertible fermionic states. Our results apply in the presence of magnetic field and Chern number $C neq 0$, in contrast to previous work.
  arXiv  Detail & Related papers  (2023-03-29T18:00:00Z)
• Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles [55.41644538483948]
  We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the transformations symmetry and the corresponding generators. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.
  arXiv  Detail & Related papers  (2023-01-13T16:25:25Z)
• Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry [85.36456486475119]
  A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
  arXiv  Detail & Related papers  (2021-11-24T15:50:22Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Classification of (2+1)D invertible fermionic topological phases with symmetry [2.74065703122014]
  We classify invertible fermionic topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups $G_f$. Our results also generalize and provide a different approach to the recent classification of fermionic symmetry-protected topological phases by Wang and Gu.
  arXiv  Detail & Related papers  (2021-09-22T21:02:07Z)
• The Geometry of Time in Topological Quantum Gravity of the Ricci Flow [41.94295877935867]
  We continue the study of nonrelativistic quantum gravity associated with a family of Ricci flow equations.<n>This topological gravity is of the cohomological type, and it exhibits an $cal N=2$ extended BRST symmetry.<n>We demonstrate a standard one-step BRST gauge-fixing of a theory whose fields are $g_ij$, $ni$ and $n$, and whose gauge symmetries consist of (i) the topological deformations of $g_ij$, and (ii) the ultralocal nonrelativistic limit of space
  arXiv  Detail & Related papers  (2020-11-12T06:57:10Z)
• Absolute anomalies in (2+1)D symmetry-enriched topological states and exact (3+1)D constructions [0.0]
  We show how to compute the anomaly for symmetry-enriched topological (SET) states of bosons in complete generality. We present an exactly solvable Hamiltonian for the system and demonstrate explicitly a (2+1)D $G$ symmetric surface termination. Our results can also be viewed as providing a method to compute the $mathcalH4(G, U(1))$ obstruction that arises in the theory of $G$-crossed braided tensor categories.
  arXiv  Detail & Related papers  (2020-03-25T18:00:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.