Slow quenches in Chern insulator ribbons

Ulčakar, Lara; Mravlje, Jernej; Rejec, T.

doi:10.1103/physrevb.100.125110

Cited by 7 publications

(5 citation statements)

References 46 publications

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“…Taking into account that zν = 1 [35], this result follows the KZ scaling. The KZ mechanism relates the characteristic length with the density of point defects n ∝ ξ −2 (t F ), making our results in agreement with earlier work [35,38,44,45], which showed that excitation density is n exc = |u1−u0| 8πτ . It is interesting to look at how the Berry curvature evolves during the quench [insets to Fig.…”

supporting

confidence: 92%

“…Topological systems have been realized in solid state [9][10][11][12][13][14][15] and in cold atoms [16][17][18][19][20][21][22][23]. Recently, a lot of attention has been given to dynamical critical properties after quenches across topological phase transitions in topological insulators [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38], superconductors [39][40][41] and p + ip superfluids [42,43]. An important observation of interest to this paper was made in Refs.…”

mentioning

confidence: 99%

“…An important observation of interest to this paper was made in Refs. [35,38,[44][45][46] which showed that the number of excitations after a slow quench follows the Kibble-Zurek (KZ) scaling.…”

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confidence: 99%

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Kibble-Zurek behavior in disordered Chern insulators

Ulčakar,

Mravlje,

Rejec

2020

Preprint

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Even though no local order parameter in the sense of the Landau theory exists for topological quantum phase transitions in Chern insulators, the highly non-local Berry curvature exhibits critical behavior near a quantum critical point. We investigate the critical properties of its real space analog, the local Chern marker, in weakly disordered Chern insulators. Due to disorder, inhomogeneities appear in the spatial distribution of the local Chern marker. Their size exhibits power-law scaling with the critical exponent matching the one extracted from the Berry curvature of a clean system. We drive the system slowly through such a quantum phase transition. The characteristic size of inhomogeneities in the non-equilibrium post-quench state obeys the Kibble-Zurek scaling. In this setting, the local Chern marker thus does behave in a similar way as a local order parameter for a symmetry breaking second order phase transition. The Kibble-Zurek scaling also holds for the inhomogeneities in the spatial distribution of excitations and of the orbital polarization.

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confidence: 92%

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confidence: 99%

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Kibble-Zurek behavior in disordered Chern insulators

Ulčakar,

Mravlje,

Rejec

2020

Preprint

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“…The experimental observations of a nonzero Hall drift [1,27] thus inspired a plethora of studies [15,25,26,[28][29][30][31][32][33][34][35][36][37][38][39][40][41]. Nonunitary effects, including thermal baths [28,30] and dephasing noise [34], were shown to stabilize a nearly quantized Hall conductance, in much the same way that a diagonal ensemble of unitary time evolution would predict [42,43].…”

Section: Introductionmentioning

confidence: 85%

Universal Landau-Zener regimes in dynamical topological phase transitions

Ge,

Rigol

2020

Preprint

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In finite systems driven unitarily across topological phase transitions, the Chern number and the Bott index have been found to exhibit different behaviors depending on the boundary conditions and on the commensurability of the lattice. For periodic boundary conditions, the Chern number does not change for finite commensurate lattices (nor in the thermodynamic limit). On the other hand, the Chern number can change for incommensurate lattices with periodic boundary conditions and the Bott index can change for lattices with open boundary conditions. Here we show that the scalings of the fields at which those two indices change exhibit Landau-Zener and near-adiabatic regimes depending on the speed at which the strength of the drive is ramped up and on the system size. Those regimes are preceded by a regime in which the topological indices do not change. The latter is the only regime that, for nonvanishing ramp speeds, survives in the thermodynamic limit. We then show that the dc Hall response can be used to detect topological phase transitions independently of the behavior of the topological indices.

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“…In experiments, the KZM of dynamical phase transitions has been observed in superfluid [68], Bose-Einstein condensation [69][70][71], trapped ions [72][73][74][75], and superconducting circuits [76,77]. Recently, considerable effort is devoted to studying the dynamical phase transitions in topological systems [78][79][80][81][82][83][84][85][86][87]. For the dynamical topological phase transition, the edge states may exhibit anomalous scaling [78][79][80] and the local Berry curvature [86] and topological marker [86] can be connected to the characteristic correlation length in the context of the KZM.…”

Section: Introductionmentioning

confidence: 99%

Topological and dynamical phase transitions in the Su–Schrieffer–Heeger model with quasiperiodic and long-range hoppings

Zhang¹,

Wu²,

Tang³

et al. 2022

Commun. Theor. Phys.

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Disorders and long-range hoppings can induce exotic phenomena in condensed matter and artificial systems. We study the topological and dynamical properties of the quasiperiodic Su-Schrier-Heeger model with long-range hoppings. It is found that the interplay of quasiperiodic disorder and long-range hopping can induce topological Anderson insulator phases with non-zero winding numbers ω=1,2, and the phase boundaries can be consistently revealed by the divergence of zero-energy mode localization length. We also investigate the nonequilibrium dynamics by ramping the long-range hopping along two different paths. The critical exponents extracted from the dynamical behavior agree with the Kibble-Zurek mechanic prediction for the path with W=0.90. In particular, the dynamical exponent of the path crossing the multicritical point is numerical obtained as 1/6∼0.167, which agrees with the unconventional finding in the previously studied XY spin model. Besides, we discuss the anomalous and non-universal scaling of the defect density dynamics of topological edge states in this disordered system under open boundary condictions.

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Slow quenches in Chern insulator ribbons

Cited by 7 publications

References 46 publications

Kibble-Zurek behavior in disordered Chern insulators

Kibble-Zurek behavior in disordered Chern insulators

Universal Landau-Zener regimes in dynamical topological phase transitions

Topological and dynamical phase transitions in the Su–Schrieffer–Heeger model with quasiperiodic and long-range hoppings

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