Multiple signatures of topological transitions for interacting fermions in chain lattices

Chan, Yang-Hao; Chiu, Ching-Kai; Sun, Kuei

doi:10.1103/physrevb.92.104514

Cited by 42 publications

(42 citation statements)

References 119 publications

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“…2(b)], thus rendering the criterion unreliable. A related criterion, namely the compressibility −∂ 2 E GS /∂μ 2 , was discussed recently [29] and shown to be insensitive to finite-size effects. However, in the disordered case the compressibility shows the same problems as the energy gap.…”

Section: Possible Criteriamentioning

confidence: 99%

“…Two of the most relevant experimental influences are disorder [10][11][12][13][14][15][16][17] and interactions [11,16,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. Concerning the effects of disorder, it has been observed that moderate disorder supports the topological phase by pinning down quasiparticles associated with the phase transition, which has been investigated in particular for the two-dimensional toric code [34][35][36].…”

Section: Introductionmentioning

confidence: 99%

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Topological order in the Kitaev/Majorana chain in the presence of disorder and interactions

2016

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We study the combined effect of interactions and disorder on topological order in one dimension. Toward that end, we consider a generalized Kitaev chain including fermion-fermion interactions and disorder in the chemical potential. We determine the phase diagram by performing density-matrix renormalization-group calculations on the corresponding spin-1/2 chain. We find that moderate disorder or repulsive interactions individually stabilize the topological order, which remains valid for their combined effect. However, both repulsive and attractive interactions lead to a suppression of the topological phase at strong disorder.

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Section: Possible Criteriamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Topological order in the Kitaev/Majorana chain in the presence of disorder and interactions

2016

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“…For example, considerable progress has been made towards developing number preserving theories of the Majorana modes, [15][16][17][18][19][20] as well as a growing body of work which examines how free-topological superconducting phases are affected by the addition of interacting electron-electron terms. [21][22][23][24][25][26][27][28][29][30][31][32][33] One aspect of this latter story is concerned with the stability and structure of the Majorana zero-modes themselves and how they are affected by the presence of density-density interaction terms that break the exactly solvable nature of the underlying model. The issue of stable zero-modes has also been addressed in the related context of 1-d parafermionic chains.…”

Section: Introductionmentioning

confidence: 99%

Multiparticle content of Majorana zero modes in the interactingp-wave wire

Kells

2015

Phys. Rev. B

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In the topological phase of p-wave superconductors, zero-energy Majorana quasi-particle excitations can be well-defined in the presence of local density-density interactions. Here we examine this phenomenon from the perspective of matrix representations of the commutator H = [H, •] ,with the aim of characterising the multiparticle content of the many-body Majorana mode. To do this we show that, for quadratic fermionic systems, H can always be decomposed into sub-blocks that act as multi-particle generalisations of the BdG/Majorana forms that encode single-particle excitations. In this picture, density-density like interactions will break this exact excitation-number symmetry, coupling different sub-blocks and lifting degeneracies so that the eigen-operators of the commutator H take the form of individual eigenstate transitions | n m |. However, the Majorana mode is special in that zero-energy transitions are not destroyed by local interactions and it becomes possible to define many-body Majoranas as the odd-parity zero-energy solutions of H that minimise their excitation number. This idea forms the basis for an algorithm which is used to characterise the multi-particle excitation content of the Majorana zero modes of the one-dimensional p-wave lattice model. We find that the multi-particle content of the Majorana zero-mode operators is significant even at modest interaction strengths. This has important consequences for the stability of Majorana based qubits when they are coupled to a heat bath. We will also discuss how these findings differ from previous work regarding the structure of the many-body-Majorana operators and point out that this should affect how certain experimental features are interpreted.

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“…Majorana zero modes have attracted intensive studies in past years [1][2][3][4][5] . This is not only due to their potential applications in topological quantum computation 6 , but also some reported experimental evidences of their existence [7][8][9][10][11][12][13][14] .…”

Section: Introductionmentioning

confidence: 99%

Characterization of topological phases of dimerized Kitaev chain via edge correlation functions

Wang¹,

Miao²,

Jin³

et al. 2017

Phys. Rev. B

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We study the interacting dimerized Kitaev chain at the symmetry point ∆ = t and the chemical potential µ = 0 under open boundary conditions, which can be exactly solved by applying two Jordan-wigner transformations and a spin rotation. By using exact analytic methods, we calculate two edge correlation functions of Majorana fermions and demonstrate that they can be used to distinguish different topological phases and characterize the topological phase transitions of the interacting system. According to the thermodynamic limit values of these two edge correlation functions, we give the phase diagram of the interacting system which includes three different topological phases: the trivial, the topological superconductor and the Su-Schrieffer-Heeger-like topological phase and we further distinguish the trivial phase by obtaining the local density distribution numerically.

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Multiple signatures of topological transitions for interacting fermions in chain lattices

Cited by 42 publications

References 119 publications

Topological order in the Kitaev/Majorana chain in the presence of disorder and interactions

Topological order in the Kitaev/Majorana chain in the presence of disorder and interactions

Multiparticle content of Majorana zero modes in the interactingp-wave wire

Characterization of topological phases of dimerized Kitaev chain via edge correlation functions

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