Simulation of a topological phase transition in a Kitaev chain with long-range coupling using a superconducting circuit

Tao, Ziyu; Yan, Tongxing; Liu, Weiyang; Niu, Jingjing; Zhou, Yuxuan; Zhang, Libo; Jia, Hao; Chen, Weiqiang; Liu, Song; Chen, Yuanzhen; Yu, Dapeng

doi:10.1103/physrevb.101.035109

“…The model discussed in this work can be efficiently simulated using the superconducting circuit of a single qubit driven by the microwave pulses [53,54] and the ultracold atoms in optical lattices [4,[55][56][57][58][59]. Therefore, using the good control over the nearest neighbors provided by these platforms one can study the results discussed in this work.…”

Section: Discussionmentioning

confidence: 99%

Topological phase transition between non-high symmetry critical phases and curvature function renormalization group

Kumar

¹

,

Kartik

²

,

Sarkar

³

2023

New J. Phys.

6

0

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The interplay between topology and criticality has been a recent interest of study in condensed matter physics. A unique topological transition between certain critical phases has been observed as a consequence of the edge modes living at criticalities. In this work, we generalize this phenomenon by investigating possible transitions between critical phases which are non-high symmetry in nature. We find the triviality and non-triviality of these critical phases in terms of the decay length of the edge modes and also characterize them using the winding numbers. The distinct non-high symmetry critical phases are separated by multicritical points with linear dispersion at which the winding number exhibits the quantized jump, indicating a change in the topology (number of edge modes) at the critical phases. Moreover, we reframe the scaling theory based on the curvature function, i.e. curvature function renormalization group method to efficiently address the non-high symmetry criticalities and multicriticalities. Using this we identify the conventional topological transition between gapped phases through non-high symmetry critical points, and also the unique topological transition between critical phases through multicritical points. The renormalization group flow, critical exponents and correlation function of Wannier states enable the characterization of non-high symmetry criticalities along with multicriticalities.

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“…The model discussed in this work can be efficiently simulated using the superconducting circuit of a single qubit driven by the microwave pulses 51,52 and the ultracold atoms in optical lattices 4,[53][54][55][56][57] . Therefore, using the good control over the nearest neighbors provided by these platforms one can study the results discussed in this work.…”

Section: Discussionmentioning

confidence: 99%

Topological phase transition between non-high symmetry critical phases and curvature function renormalization group

Kumar¹,

Kartik²,

Sarkar³

2022

Preprint

0

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The interplay between topology and criticality has been a recent interest of study in condensed matter physics. A unique topological transition between certain critical phases has been observed as a consequence of the edge modes living at criticalities. In this work, we generalize this phenomenon by investigating possible transitions between critical phases which are non-high symmetry in nature. We find the triviality and non-triviality of these critical phases in terms of the decay length of the edge modes and also characterize them using the winding numbers. The distinct non-high symmetry critical phases are separated by multicritical points with linear dispersion at which the winding number exhibits the quantized jump, indicating a change in the topology (number of edge modes) at the critical phases. Moreover, we reframe the scaling theory based on the curvature function, i.e. curvature function renormalization group method to efficiently address the non-high symmetry criticalities and multicriticalities. Using this we identify the conventional topological transition between gapped phases through non-high symmetry critical points, and also the unique topological transition between critical phases through multicritical points. The renormalization group flow, critical exponents and correlation function of Wannier states enable the characterization of non-high symmetry criticalities along with multicriticalities.

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“…The long-range nature can even change the effective dimension of the system 15 , 16 , as well as can create a transition between two topological phases without gap closing in case of topological systems 17 . Long-range models also a field of curiosity from the perspective of bulk-boundary correspondence 18 , simulation of superconducting circuits 19 , quantum information propagation 20 and topology at finite temperature 21 .…”

Section: Introductionmentioning

confidence: 99%

Critical scaling of a two-orbital topological model with extended neighboring couplings

Kartik,

Kumar,

Sarkar

2024

Sci Rep

0

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Extended-range models are the interesting systems, which has been widely used to understand the non-local properties of the fermions at quantum scale. We aim to study the interplay between criticality and extended range couplings under various symmetry constraints. Here, we consider a two orbital Bernevig–Hughes–Zhang model in one dimension with longer (finite neighbor) and long-range (infinite neighbor) couplings. We study the behavior of model using scaling laws and universality class for models with Hermitian, parity-time ($$\mathscr{P}\mathscr{T}$$ P T ) symmetric and broken time-reversal symmetries. We observe the interesting results on multi-criticalities, where the universality class of critical exponent is different than the normal criticalities. Also, the results can be generalized by considering the interplay between criticalities and different symmetry classes of Hamiltonian. Also, with the introduction of extended-range of coupling, there occurs different criticalities, and we provide the analogy to characterize their universality classes. We also show the violation of Lorentz invariance at multi-criticalities and evaluation of short-range limit in long-range models as the highlights of this work.

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Simulation of a topological phase transition in a Kitaev chain with long-range coupling using a superconducting circuit

Cited by 14 publications

References 52 publications

Topological phase transition between non-high symmetry critical phases and curvature function renormalization group

Topological phase transition between non-high symmetry critical phases and curvature function renormalization group

Topological phase transition between non-high symmetry critical phases and curvature function renormalization group

Critical scaling of a two-orbital topological model with extended neighboring couplings

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