Fidelity susceptibility near topological phase transitions in quantum walks

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

doi:10.1103/physrevb.102.134111

Cited by 29 publications

(24 citation statements)

References 48 publications

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“…which is found to be equal to the square of the stroboscopic Berry curvature F (k) for any parametrization of d(k) [58,93,94]. We now detail the first type of TPT occurred in the periodically driven Kitaev model.…”

Section: A Correlation Function and Fidelity Susceptibility For Periodically Driven Kitaev Modelmentioning

confidence: 95%

“…[73][74][75][76], here we follow the approach of Ref. [58], which demonstrated that a fidelity susceptibility that describes the evolution of Bloch eigenstate in momentum space can better interpret the scaling law between the exponents γ and ν. To do this, we consider the change in the filled band Bloch eigenstate |u − (k) under a momentum shift k to k + δk s along the scaling direction.…”

Section: Correlation Function and Fidelity Susceptibility For Static Kitaev Modelmentioning

confidence: 99%

“…In this work, we aim to study TPTs in both the static and periodically driven 2D Kitaev models hosting MMs. We classify these transitions from the perspective of universality using two measures: (i) a Majorana version of a recently proposed stroboscopic Wannier state correlation function [38,[55][56][57], which encodes the notion of a correlation length that diverges at the TPT and (ii) a momentum-dependent fidelity susceptibility that measures the distance between Bloch states in the momentum space [58]. Our classification reveals the existence of cross-dimensional universality classes.…”

Section: Introductionmentioning

confidence: 99%

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Crossdimensional universality classes in static and periodically driven Kitaev models

et al. 2021

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The Kitaev model on the honeycomb lattice is a paradigmatic system known to host a wealth of nontrivial topological phases and Majorana edge modes. In the static case, the Majorana edge modes are nondispersive. When the system is periodically driven in time, such edge modes can disperse and become chiral. We obtain the full phase diagram of the driven model as a function of the coupling and the driving period. We characterize the quantum criticality of the different topological phase transitions in both the static and driven model via the notions of Majorana-Wannier state correlation functions and momentum-dependent fidelity susceptibilities. We show that the system hosts crossdimensional universality classes: although the static Kitaev model is defined on a two-dimensional (2D) honeycomb lattice, its criticality falls into the universality class of one-dimensional (1D) linear Dirac models. For the periodically driven Kitaev model, in addition to the universality class of prototype 2D linear Dirac models, an additional 1D nodal loop type of criticality exists owing to emergent time-reversal and mirror symmetries, indicating the possibility of engineering multiple universality classes by periodic driving. The manipulation of time-reversal symmetry allows the periodic driving to control the chirality of the Majorana edge states.

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Section: A Correlation Function and Fidelity Susceptibility For Periodically Driven Kitaev Modelmentioning

confidence: 95%

Section: Correlation Function and Fidelity Susceptibility For Static Kitaev Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Crossdimensional universality classes in static and periodically driven Kitaev models

et al. 2021

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“…Here, for each pair [p, q] we have a counterpart tight-binding Hamiltonian in real space which is also able to describe a Hopf insulator model if p and q are prime to each other. We have performed a study of the energy spectra for values of p, and q from [p, q] = [1, 1] to [8,8]. For all cases, we identify the gap-closing points at critical parameter h c = −3, −1, 1, 3 following the high-symmetry points of Eq.…”

Section: Universality Class For Hopf Insulators: Beyond Z = 2 Dynamic Critical Exponentmentioning

confidence: 99%

“…In this case there is no symmetry breaking associated with an ordered phase when the system undergoes a TPT 6 . For this reason, many different approaches have been proposed recently to identify the universality classes of topological transitions using scaling ideas [6][7][8][9][10][11][12][13][14][15][16][17][18] .…”

Section: Introductionmentioning

confidence: 99%

Anisotropic scaling in 3D topological models: fromWeyl semimetal to Hopf insulator

Rufo

Griffith

Lopes

et al. 2021

Preprint

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A proposal to study topological models beyond the standard topological classification and that exhibit breakdown of Lorentz invariance is presented. The focus of the investigation relies on their anisotropic quantum critical behavior. We study anisotropic effects on three-dimensional (3D) topological models, computing their anisotropic correlation length critical exponent ν obtained from numerical calculations of the penetration length of the zero-energy surface states as a function of the distance to the topological quantum critical point. A generalized Weyl semimetal model with broken time-reversal symmetry is introduced and studied using a modified Dirac equation. An approach to characterize topological surface states in topological insulators when applied to Fermi arcs allows to capture the anisotropic critical exponent θ = νx/νz. We also consider the Hopf insulator model, for which the study of the topological surface states yields unusual values for ν and for the dynamic critical exponent z. From an analysis of the energy dispersions, we propose a scaling relation να¯ zα¯ = 2q and θ = νx/νz = zz/zx for ν and z that only depends on the Hopf insulator Hamiltonian parameters p and q and the axis direction α¯ . An anisotropic quantum hyperscaling relation is also obtained.

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Multi-critical topological transition at quantum criticality

Kumar

Kartik

Sinha

et al. 2021

Sci Rep

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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 consider transverse field Ising model with three spin interaction in one dimension and observe a topological transition between gapless phases on one of the critical lines of this model. We study the distinct nature of these gapless phases and show that they belong to different universality classes. The topological invariant number (winding number) characterize different topological phases for the different regime of parameter space. 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. The model Hamiltonian which we study is more applicable for the system with gapless excitations, where the conventional concept of topological quantum phase transition fails.

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Fidelity susceptibility near topological phase transitions in quantum walks

Cited by 29 publications

References 48 publications

Crossdimensional universality classes in static and periodically driven Kitaev models

Crossdimensional universality classes in static and periodically driven Kitaev models

Anisotropic scaling in 3D topological models: fromWeyl semimetal to Hopf insulator

Multi-critical topological transition at quantum criticality

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