Construction and classification of point-group symmetry-protected topological phases in two-dimensional interacting fermionic systems

Zhang, Jian-Hao; Yang, Shuming; Qi, Yang; Gu, Zheng-Cheng

doi:10.1103/physrevb.101.100501

Cited by 29 publications

(29 citation statements)

References 62 publications

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“…Second, it is also interesting to extend the folding approach to other spatial symmetries, such as rotation. The bulk state of rotation and other spatial SPT phases have been explored in a similar spirit to this work recently [106,107]. Extending these studies in presence of a surface would be interesting.…”

Section: Discussionmentioning

confidence: 84%

Anomaly indicators and bulk-boundary correspondences for 3D interacting topological crystalline phases with mirror and continuous symmetries

Ning,

Mao,

et al. 2021

Preprint

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We derive a series of quantitative bulk-boundary correspondences for 3D bosonic and fermionic symmetry-protected topological (SPT) phases under the assumption that the surface is gapped, symmetric and topologically ordered, i.e., a symmetry-enriched topological (SET) state. We consider those SPT phases that are protected by the mirror symmetry and continuous symmetries that form a group of U (1), SU (2) or SO(3). In particular, the fermionic cases correspond to a crystalline version of 3D topological insulators and topological superconductors in the famous ten-fold-way classification, with the time-reversal symmetry replaced by the mirror symmetry and with strong interaction taken into account. For surface SETs, the most general interplay between symmetries and anyon excitations is considered. Based on the previously proposed dimension reduction and folding approaches, we re-derive the classification of bulk SPT phases and define a complete set of bulk topological invariants for every symmetry group under consideration, and then derive explicit expressions of the bulk invariants in terms of surface topological properties (such as topological spin, quantum dimension) and symmetry properties (such as mirror fractionalization, fractional charge or spin). These expressions are our quantitative bulk-boundary correspondences. Meanwhile, the bulk topological invariants can be interpreted as anomaly indicators for the surface SETs which carry 't Hooft anomalies of the associated symmetries whenever the bulk is topologically non-trivial. Hence, the quantitative bulk-boundary correspondences provide an easy way to compute the 't Hooft anomalies of the surface SETs. Moreover, our anomaly indicators are complete. Our derivations of the bulk-boundary correspondences and anomaly indicators are explicit and physically transparent. The anomaly indicators obtained in this work can be straightforwardly translated to their timereversal counterparts that apply to the usual topological insulators and topological superconductors, due to a known correspondence between mirror and time-reversal topological phases.

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Section: Discussionmentioning

confidence: 84%

Anomaly indicators and bulk-boundary correspondences for 3D interacting topological crystalline phases with mirror and continuous symmetries

Ning,

Mao,

et al. 2021

Preprint

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“…This allows us to express U(g, k, k ⊥ ) for g ∈ G C unitary as U(g, k, k ⊥ ) = (g, k) (27) and for g ∈ G C antiunitary as…”

Section: B41 Dimensional Raising From a Symmetry Class With Chiral Antisymmetrymentioning

confidence: 99%

Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors

2021

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We study a link between the ground-state topology and the topology of the lattice via the presence of anomalous states at disclinations -- topological lattice defects that violate a rotation symmetry only locally. We first show the existence of anomalous disclination states, such as Majorana zero-modes or helical electronic states, in second-order topological phases by means of Volterra processes. Using the framework of topological crystals to construct d-dimensional crystalline topological phases with rotation and translation symmetry, we then identify all contributions to (d-2)-dimensional anomalous disclination states from weak and first-order topological phases. We perform this procedure for all Cartan symmetry classes of topological insulators and superconductors in two and three dimensions and determine whether the correspondence between bulk topology, boundary signatures, and disclination anomaly is unique.

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“…(3)By applying the fermionic crystalline equivalence [32][33][34][35][36][37] where a mirror reflection symmetry action should be mapped onto a time-reversal symmetry action, and that spinless (spin-1/2) fermionic systems should be mapped into spin-1/2 (spinless) fermionic systems, we can also derive the complete interacting classification of 2D crystalline topological insulators. In Supplementary Material, we list the classification results for all 17 wall paper groups.…”

mentioning

confidence: 99%

Exactly solvable lattice models for interacting electronic insulators in two dimensions

Yang¹,

Chen²,

Cheng³

et al. 2021

Preprint

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In the past decade, tremendous efforts have been made towards understanding fermionic symmetry protected topological (FSPT) phases in interacting systems. Nevertheless, for systems with continuum symmetry, e.g., electronic insulators, it is still unclear how to construct an exactly solvable model with a finite dimensional Hilbert space in general. In this paper, we give a lattice model construction and classification for 2D interacting electronic insulators. Based on the physical picture of U(1) f -charge decorations, we illustrate the key idea by considering the well known 2D interacting topological insulator. Then we generalize our construction to an arbitrary 2D interacting electronic insulator with symmetry G f = U(1) f ρ 1 ,ω 2 G, where U(1) f is the charge conservation symmetry and ρ1, ω2 are additional data which fully characterize the group structure of G f . Finally we study more examples, including the full interacting classification of 2D crystalline topological insulators.

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Construction and classification of point-group symmetry-protected topological phases in two-dimensional interacting fermionic systems

Cited by 29 publications

References 62 publications

Anomaly indicators and bulk-boundary correspondences for 3D interacting topological crystalline phases with mirror and continuous symmetries

Anomaly indicators and bulk-boundary correspondences for 3D interacting topological crystalline phases with mirror and continuous symmetries

Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors

Exactly solvable lattice models for interacting electronic insulators in two dimensions

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