Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation

Fraxanet, Joana; Bhattacharya, Utso; Graß, Tobias; Rakshit, Debraj; Lewenstein, Maciej; Dauphin, Alexandre

doi:10.1103/physrevresearch.3.013148

Cited by 26 publications

(19 citation statements)

References 144 publications

(119 reference statements)

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“…[20,21] which, by construction, can capture non-integral winding numbers (see Ref. [22] for a comparison with other common algorthims). Following this construction, we define a homotopic flat band Hamiltonian of the form…”

Section: B Computation Of the Real Space Winding Numbermentioning

confidence: 99%

Kitaev Chain with a Fractional Twist

Basa,

La Nave,

Phillips

2022

Preprint

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The topological non-triviality of insulating phases of matter are by now well understood through topological K-theory where the indices of the Dirac operators are assembled into topological classes. We consider in the context of the Kitaev chain a notion of a generalized Dirac operator where the associated Clifford algebra is centrally extended. We demonstrate that the central extension is achieved via taking rational operator powers of Pauli matrices that appear in the corresponding BdG Hamiltonian. Doing so introduces a pseudo-metallic component to the topological phase diagram within which the winding number is valued in Q. We find that this phase hosts a mode that remains extended in the presence of weak disorder, motivating a topological interpretation of a non-integral winding number. We remark that this is in correspondence with Ref.[1] demonstrating that projective Dirac operators defined in the absence of spin C structure have rational indices.

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Section: B Computation Of the Real Space Winding Numbermentioning

confidence: 99%

Kitaev Chain with a Fractional Twist

Basa,

La Nave,

Phillips

2022

Preprint

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“…The quasiperiodic system possesses a long-range periodicity, which is intermediate between that of the clean and randomly disordered cases, offering a rich playground to study quasiperiodic QCPs and unusual characteristic features, such as hierarchical energy spectra [23][24][25] and localization-delocalization transitions. A paradigmatic * wlyou@nuaa.edu.cn model of the quasiperiodic system is the Aubry-André-Harper (AAH) model [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45], in which the quasiperiodicity is embodied in the form of a cosine modulation incommensurate with lattice spacing. With the rapid development of experimental technologies, the AAH model can be realized in optical waveguide lattices [46][47][48], photonic crystals [49][50][51] and cold atom systems [52].…”

Section: Introductionmentioning

confidence: 99%

“…For instance, the AAH Hamiltonian has been experimentally realized by cold atomic gases in a one-dimensional optical lattice perturbed by another weak incommensurate optical lattice [52]. These feasible platforms allow us to explore the emerging topological states of matter with additional interactions in incommensurate systems, including modulated off-diagonal hopping [29], nearest neighbor p-wave superconductivity [53], a long-range p-wave superconducting pairing [34], and many-body interactions [38,54].…”

Section: Introductionmentioning

confidence: 99%

Quantum criticality and universality in the $p$-wave paired Aubry-André-Harper model

Lv,

Yi,

et al. 2022

Preprint

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We investigate the quantum criticality and universality in Aubry-André-Harper (AAH) model with p-wave superconducting pairing ∆ in terms of the generalized fidelity susceptibility (GFS). We show that the higher-order GFS is more efficient in spotlighting the critical points than lowerorder ones, and thus the enhanced sensitivity is propitious for extracting the associated universal information from the finite-size scaling in quasiperiodic systems. The GFS obeys power-law scaling for localization transitions and thus scaling properties of the GFS provide compelling values of critical exponents. Specifically, we demonstrate that the fixed modulation phase φ = π alleviates the odd-even effect of scaling functions across the Aubry-André transition with ∆ = 0, while the scaling functions for odd and even numbers of system sizes with a finite ∆ cannot coincide irrespective of the value of φ. A thorough numerical analysis with odd number of system sizes reveals the correlationlength exponent ν 1.000 and the dynamical exponent z 1.388 for transitions from the critical phase to the localized phase, suggesting the unusual universality class of localization transitions in the AAH model with a finite p-wave superconducting pairing lies in a different universality class from the Aubry-André transition. The results may be testified in near term state-of-the-art experimental settings.

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“…So far, the robustness of topological phases in the Kitaev chain has been mainly characterized by studying the fate of Majorana modes when including sufficiently strong local perturbations such as spatial inhomogeneities [14][15][16][17][18][19][20][21], eventually also in the presence of interaction [22][23][24] or long-range pairing [25][26][27]. However, besides the presence of edge states, the Kitaev model is also characterized by non-trivial quantum entanglement properties [28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Robust multipartite entanglement in dirty topological wires

Pezzé¹,

Lepori²

2022

Preprint

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Identifying and characterizing quantum phases of matter in the presence of long range correlations and/or spatial disorder is, generally, a challenging and relevant task. Here, we study a generalization of the Kiteav chain with variable-range pairing and different site-dependence of the chemical potential, addressing commensurable and incommensurable modulations as well as Anderson disorder. In particular, we analyze multipartite entanglement (ME) in the ground state of the dirty topological wires by studying the scaling of the quantum Fisher information (QFI) with the system's size. For nearest-neighbour pairing the Heisenberg scaling of the QFI is found in one-to-one correspondence with topological phases hosting Majorana modes. For finite-range pairing, we recognize long-range phases by the super-extensive scaling of the QFI and characterize complex lobe-structured phase diagrams. Overall, we observe that ME is robust against finite strengths of spatial inhomogeneity. This work contributes to establish ME as a central quantity to study intriguing aspects of topological systems.

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Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation

Cited by 26 publications

References 144 publications

Kitaev Chain with a Fractional Twist

Kitaev Chain with a Fractional Twist

Quantum criticality and universality in the $p$-wave paired Aubry-André-Harper model

Robust multipartite entanglement in dirty topological wires

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