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

Gergs, Niklas M.; Fritz, Lars; Schuricht, Dirk

doi:10.1103/physrevb.93.075129

Cited by 73 publications

(77 citation statements)

References 50 publications

(128 reference statements)

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“…The issue now would be to cast parity effects in terms of a many-body generalization of the non-interacting case 125,131,132 . A possible approach would entail drawing from the exact map between the Kitaev chain Hamiltonian with nearest neighbor density-density interaction and the transverse-field XYZ Heisenberg spin chain [133][134][135] . Such systems with both disorder and interactions have also been studied actively in the recent years in the context of many-body localization.…”

Section: Discussionmentioning

confidence: 99%

Majorana wave-function oscillations, fermion parity switches, and disorder in Kitaev chains

Hegde¹,

Vishveshwara²

2016

Phys. Rev. B

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We study the decay and oscillations of Majorana fermion wavefunctions and ground state (GS) fermion parity in one-dimensional topological superconducting lattice systems. Using a Majorana transfer matrix method, we find that Majorana wavefunction properties are encoded in the associated Lyapunov exponent, which in turn is the sum of two independent components: a 'superconducting component' which characterizes the gap induced decay, and the 'normal component', which determines the oscillations and response to chemical potential configurations. The topological phase transition separating phases with and without Majorana end modes is seen to be a cancellation of these two components. We show that Majorana wavefunction oscillations are completely determined by an underlying non-superconducting tight-binding model and are solely responsible for GS fermion parity switches in finite-sized systems. These observations enable us to analytically chart out wavefunction oscillations, the resultant GS parity configuration as a function of parameter space in uniform wires, and special parity switch points where degenerate zero energy Majorana modes are restored in spite of finite size effects. For disordered wires, we find that band oscillations are completely washed out leading to a second localization length for the Majorana mode and the remnant oscillations are randomized as per Anderson localization physics in normal systems. Our transfer matrix method further allows us to i) reproduce known results on the scaling of mid-gap Majorana states and demonstrate the origin of its log-normal distribution, ii) identify contrasting behavior of disorder-dependent GS parity switches for the cases of even versus odd number of lattice sites, and iii) chart out the GS parity configuration and associated parity switch points as a function of disorder strength.

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Section: Discussionmentioning

confidence: 99%

Majorana wave-function oscillations, fermion parity switches, and disorder in Kitaev chains

Hegde¹,

Vishveshwara²

2016

Phys. Rev. B

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“…The existence of Majorana zero modes is of special interest because it can be applied to the physical construction of qubits for topological quantum computing [13][14][15] . From an experimental point of view, it is essential to investigate the effects of disorder [16][17][18][19][20] and interactions [21][22][23][24][25][26][27][28][29][30][31][32] . Furthermore, various theoretical aspects have been revealed, including the connection with supersymmetry 30,31,[33][34][35] , the generalization to parafermion modes [36][37][38][39][40][41][42][43] , and the construction of topologically invariant defects 44 .…”

Section: Introductionmentioning

confidence: 99%

Exact zero modes in twisted Kitaev chains

Kawabata

Kobayashi

et al. 2017

Phys. Rev. B

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We study the Kitaev chain under generalized twisted boundary conditions, for which both the amplitudes and the phases of the boundary couplings can be tuned at will. We explicitly show the presence of exact zero modes for large chains belonging to the topological phase in the most general case, in spite of the absence of "edges" in the system. For specific values of the phase parameters, we rigorously obtain the condition for the presence of the exact zero modes in finite chains, and show that the zero modes obtained are indeed localized. The full spectrum of the twisted chains with zero chemical potential is analytically presented. Finally, we demonstrate the persistence of zero modes (level crossing) even in the presence of disorder or interactions.

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“…Such techniques can be implemented in different ways. One such way is Density Matrix Renormalization Group (DMRG) [7,8,17,18], which minimizes the energy over the space of eigenstates of the chain's local density matrices. Another approach is to use a tensor representation as a variational network in an abstract way.…”

Section: Introductionmentioning

confidence: 99%

End-to-end correlations in the Kitaev chain

Reslen

2018

J. Phys. Commun.

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The interdependence between long range correlations and topological signatures in fermionic arrays is examined. End-to-end correlations, in particular those accounting for the hopping between the chain edges, maintain a characteristic pattern in the presence of delocalized excitations. This feature can be used as an operational criterion to identify Majorana fermions in one-dimensional systems. The study discusses how to obtain the chain eigenstates in tensor-state representation as well as the correlations. Outstandingly, the final result can be written as a simple analytical expression that underlines the link with the system's topological phases.

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

Cited by 73 publications

References 50 publications

Majorana wave-function oscillations, fermion parity switches, and disorder in Kitaev chains

Majorana wave-function oscillations, fermion parity switches, and disorder in Kitaev chains

Exact zero modes in twisted Kitaev chains

End-to-end correlations in the Kitaev chain

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