Real-space recipes for general topological crystalline states

Song, Zhida; Fang, Chen; Qi, Yang

doi:10.1038/s41467-020-17685-5

Cited by 64 publications

(71 citation statements)

References 63 publications

(132 reference statements)

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“…Our construction (see Fig. 1) is similar to some constructions of SPT and SET phases [45][46][47][48]. It is also similar to the layer, cage-net, or string-membrane constructions of fracton phases [49][50][51][52][53][54].…”

Section: Introductionmentioning

confidence: 60%

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Systematic construction of gapped nonliquid states

Wen

2020

Phys. Rev. Research

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Using Abelian and non-Abelian topological orders in two-dimensional (2D) space and the different ways to glue them together via their gapped boundaries, we propose a systematic way to construct three-dimensional (3D) gapped states (and in other dimensions). The resulting states are called cellular topological states, which include gapped nonliquid states, as well as gapped liquid states in some special cases. Some new fracton states with fractal excitations are constructed even using 2D Z 2 topological order. More general cellular topological states can be constructed by connecting 2D domain walls between different 3D topological orders. The constructed cellular topological states can be viewed as fixed-point states for a reverse renormalization of gapped nonliquid states.

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Section: Introductionmentioning

confidence: 60%

“…We also need to choose (anomalous) topological orders in various dimensions to have the proper symmetries, as discussed in Refs. [45][46][47][48].…”

Section: Reverse Renormalization and Generic Constructionmentioning

confidence: 99%

Systematic construction of gapped nonliquid states

Wen

2020

Phys. Rev. Research

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“…More importantly, we find two new types of TSC phases in the superconducting wire with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$C_{4z}\mathcal {T}$\end{document} or \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$C_{6z}\mathcal {T}$\end{document} , which are beyond the already known AZ classes and can be characterized by Z h or Z h ⊕ Z c topological invariants, respectively. These results not only enrich the variety of the 1D TSC, but also provide luxuriant building blocks for the construction of new type 2D and 3D TSCs, by following the general method proposed in [ 46 ]. For example, one can couple the 1D TSCs in the y direction to construct a 2D TSC.…”

Section: Discussionmentioning

confidence: 90%

New types of topological superconductors under local magnetic symmetries

Zou

Xie

Song

et al. 2020

National Science Review

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We classify gapped topological superconducting (TSC) phases of one-dimensional quantum wires with local magnetic symmetries (LMSs), in which the time-reversal symmetry $\mathcal {T}$ is broken but its combinations with certain crystalline symmetry such as $M_x \mathcal {T}$, $C_{2z} \mathcal {T}$, $C_{4z}\mathcal {T}$, and $C_{6z}\mathcal {T}$ are preserved. Our results demonstrate that an equivalent BDI class TSC can be realized in the $M_x \mathcal {T}$ or $C_{2z} \mathcal {T}$ superconducting wire, which is characterized by a chiral Zc invariant. More interestingly, we also find two types of totally new TSC phases in the $C_{4z}\mathcal {T}$, and $C_{6z}\mathcal {T}$ superconducing wires, which are beyond the known AZ class, and are characterized by a helical Zh invariant and Zh⊕Zc invariants, respectively. In the Zh TSC phase, Z-pairs of MZMs are protected at each end. In the $C_{6z}\mathcal {T}$ case, the MZMs can be either chiral or helical, and even helical-chiral coexisting. The minimal models preserving $C_{4z}\mathcal {T}$ or $C_{6z}\mathcal {T}$ symmetry are presented to illustrate their novel TSC properties and MZMs.

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“…where |ψ s j, j = 1 √ 3 (|00 j, j + |11 j, j + |22 j, j ). Although every unit cell hosts a nontrivial projective representation, this system does not have an LSM anomaly [41][42][43], and it turns out that one can construct a gapped symmetric ground state. This symmetric phase is actually an SPT phase characterized by a fractionalized entanglement spectrum; as such, there is no simple classical picture of this state.…”

Section: B Classical Picture Of Phasesmentioning

confidence: 99%

One-dimensional model for deconfined criticality with Z3×Z3 symmetry

2021

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We continue recent efforts to discover examples of deconfined quantum criticality in one-dimensional models. In this work we investigate the transition between a Z 3 ferromagnet and a phase with valence bond solid (VBS) order in a spin chain with Z 3 × Z 3 global symmetry. We study a model with alternating projective representations on the sites of the two sublattices, allowing the Hamiltonian to connect to an exactly solvable point having VBS order with the character of SU(3)-invariant singlets. Such a model does not admit a Lieb-Schultz-Mattis theorem typical of systems realizing deconfined critical points. Nevertheless, we find evidence for a direct transition from the VBS phase to a Z 3 ferromagnet. Finite-entanglement scaling data are consistent with a second-order or weakly first-order transition. We find in our parameter space an integrable lattice model apparently describing the phase transition, with a very long, finite, correlation length of 190878 lattice spacings. Based on exact results for this model, we propose that the transition is extremely weakly first order and is part of a family of deconfined quantum critical points described by walking of renormalization group flows.

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Real-space recipes for general topological crystalline states

Cited by 64 publications

References 63 publications

Systematic construction of gapped nonliquid states

Systematic construction of gapped nonliquid states

New types of topological superconductors under local magnetic symmetries

One-dimensional model for deconfined criticality with Z3×Z3 symmetry

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