Fidelity susceptibility near topological phase transitions in quantum walks

Panahiyan, S.; Chen, W.; Fritzsche, S.

doi:10.48550/arxiv.2007.10669

Cited by 2 publications

(2 citation statements)

References 50 publications

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“…( 8), since for a point M, one is only required to calculate the curvature function at three points F (M, k 0 +∆k), F (M, k 0 ) and F (M + ∆M i Mi , k 0 ) to obtain the RG flow along the Mi direction. The CRG is, therefore, a powerful tool to capture TQPTs in a multi-dimensional parameter space, as has been demonstrated for Floquet systems and interacting systems [41][42][43][44][45] .…”

Section: Curvature Renormalization Group Approachmentioning

confidence: 99%

Scaling behavior in a multicritical one-dimensional topological insulator

2020

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A class of Aubry-André-Harper models of spin-orbit coupled electrons exhibits a topological phase diagram where two regions belonging to the same phase are split up by a multicritical point. The critical lines which meet at this point each defines a topological quantum phase transition with a second-order nonanalyticity of the ground-state energy, accompanied by a linear closing of the spectral gap with respect to the control parameter; except at the multicritical point which supports fourth-order transitions with parabolic gap-closing. Here both types of criticality are characterized through a scaling analysis of the curvature function defined from the topological invariant of the model. We extract the critical exponents of the diverging curvature function at the nonhigh symmetry points in the Brillouin zone where the gap closes, and also apply a renormalization group approach to the flattening curvature function at high symmetry points. We also derive a basis-independent correlation function between Wannier states to characterize the transition. Intriguingly, we find that the critical exponents and scaling law defined with respect to the spectral gap remain the same regardless of the order of the transition.

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Section: Curvature Renormalization Group Approachmentioning

confidence: 99%

Scaling behavior in a multicritical one-dimensional topological insulator

2020

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“…In one dimensional systems this scaling procedure is analogous to stretching a string until the knots are revealed [28]. This curvature function renormalization group (CRG) has been used in studying the topological phase transition in, Kitaev model, Su-Schrieffer-Heeger model [25], periodically driven systems [27,29], systems without inversion symmetry [30], models with Z 2 invariant [31], quantum walks that simulate one and two-dimensional Dirac models [32], and also in interacting systems [21,33] etc. All these characterizing tools mentioned above have been widely used to distinguish between gapped phases separated by a topological transition.…”

Section: Introductionmentioning

confidence: 99%

Multi-critical topological transition at quantum criticality

Kumar,

Kartik,

Rahul

et al. 2020

Preprint

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The investigation and characterization of topological quantum phase transition between gapless phases is one of the recent interest of research in topological states of matter. We observe a topological transition between gapless phases on one of the critical line of our model Hamiltonian. We study the distinct nature of these gapless phases and show that they belong to different universality classes. We observe the evidence of two multi-critical points, one is topologically trivial and the other one is topologically active. Topological quantum phase transition between the gapless phases on the critical line occurs through the non-trivial multi-critical point in the Lifshitz universality class. We calculate and analyze the behavior of Wannier state correlation function close to the multi-critical point and confirm the topological transition between gapless phases. We show the breakdown of Lorentz invariance at this multi-critical point through the energy dispersion analysis. We also show that the scaling theories and curvature function renormalization group can also be effectively used to understand the topological quantum phase transitions between gapless phases.

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Fidelity susceptibility near topological phase transitions in quantum walks

Cited by 2 publications

References 50 publications

Scaling behavior in a multicritical one-dimensional topological insulator

Scaling behavior in a multicritical one-dimensional topological insulator

Multi-critical topological transition at quantum criticality

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