Topological Anderson insulator phase in a quasicrystal lattice

Chen, Rui; Xu, Dong-Hui; Zhou, Bin

doi:10.1103/physrevb.100.115311

Cited by 57 publications

(33 citation statements)

References 72 publications

(104 reference statements)

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“…First, such long-range interactions are known to have profound effects on the universality, and indeed, even the existence, of many phase transitions [39][40][41][42][43][44]; in addition, long-range interactions can parametrically alter the form of Lieb-Robinson bounds and scrambling lightcones [45][46][47][48]. Second, many of the most promising experimental platforms for investigating the measurementinduced transition, including Rydberg tweezer arrays, polar molecules, trapped ions and solid-state magnetic dipoles, inherently feature long-range interactions [49][50][51][52][53].…”

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confidence: 99%

The Measurement-induced Transition in Long-range Interacting Quantum Circuits

Block,

Bao,

Choi

et al. 2021

Preprint

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The competition between scrambling unitary evolution and projective measurements leads to a phase transition in the dynamics of quantum entanglement. Here, we demonstrate that the nature of this transition is fundamentally altered by the presence of long-range, power-law interactions. For sufficiently weak power-laws, the measurement-induced transition is described by conformal field theory, analogous to short-range-interacting hybrid circuits. However, beyond a critical power-law, we demonstrate that long-range interactions give rise to a continuum of non-conformal universality classes, with continuously varying critical exponents. We numerically determine the phase diagram for a one-dimensional, long-range-interacting hybrid circuit model as a function of the power-law exponent and the measurement rate. Finally, by using an analytic mapping to a long-range quantum Ising model, we provide a theoretical understanding for the critical power-law.

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confidence: 99%

The Measurement-induced Transition in Long-range Interacting Quantum Circuits

Block,

Bao,

Choi

et al. 2021

Preprint

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“…Following our work, Chen et al studied the effect of disorder on the QSH state in quasicrystals and found that disorder-induced topological Anderson insulators can also be realized in quasicrystals [43,44]. Based on the model in Eq.…”

Section: Quantum Spin Hall Statesmentioning

confidence: 87%

Topological states in quasicrystals

Fan,

Huang

2021

Preprint

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With the rapid development of topological states in crystals, the study of topological states has been extended to quasicrystals in recent years. In this review, we summarize the recent progress of topological states in quasicrystals, particularly focusing on one-dimensional (1D) and 2D systems. We first give a brief introduction to quasicrystalline structures. Then, we discuss topological phases in 1D quasicrystals where the topological nature is attributed to the synthetic dimensions associated with the quasiperiodic order of quasicrystals. We further present the generalization of various types of crystalline topological states to 2D quasicrystals, where real-space expressions of corresponding topological invariants are introduced due to the lack of translational symmetry in quasicrystals. Finally, since quasicrystals possess forbidden symmetries in crystals such as five-fold and eight-fold rotation, we provide an overview of unique quasicrystalline symmetry-protected topological states without crystalline counterpart.

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“…In recent years, the TAIs and their generalizations have been revealed in various systems [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], even in some non-Hermitian systems [31][32][33][34][35][36][37] and in the presence of inter-particle interactions [38][39][40]. Some of them have been experimentally observed in engineered lattices, such as cold atomic gases [41], photonic and sonic crystals [42][43][44], electric circuits [45], and photonic quantum walks [36].…”

Section: Introductionmentioning

confidence: 99%

Topological Anderson insulators with different bulk states in quasiperiodic chains

Tang,

Liu,

Zhang

et al. 2022

Preprint

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We investigate the topology and localization of one-dimensional Hermitian and non-Hermitian Su-Schrieffer-Heeger chains with quasiperiodic hopping modulations. In the Hermitian case, phase diagrams are obtained by numerically and analytically calculating various topological and localization characters. We show the presence of topological extended, intermediate, and localized phases due to the coexistence of topological and localization phase transitions driven by the quasiperiodic disorder. In particular, we uncover three types of disorder-induced topological Anderson insulators (TAIs) with extended, intermediate, and localized bulk states in this chiral chain. Moreover, we study the non-Hermitian effects on the TAIs by considering two kinds of non-Hermiticities from the non-conjugate complex hopping phase and asymmetric hopping strength, respectively. We demonstrate that three types of TAIs preserve under the non-Hermitian perturbations with some unique localization and topological properties, such as the non-Hermitian real-complex and localization transitions and their topological nature.

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Topological Anderson insulator phase in a quasicrystal lattice

Cited by 57 publications

References 72 publications

The Measurement-induced Transition in Long-range Interacting Quantum Circuits

The Measurement-induced Transition in Long-range Interacting Quantum Circuits

Topological states in quasicrystals

Topological Anderson insulators with different bulk states in quasiperiodic chains

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