Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Z2 topological order and topological protection of majorana fermion qubits. / Haq, Rukhsan Ul; Kauffman, Louis H.
в: Condensed Matter, Том 6, № 1, 11, 03.2021, стр. 1-22.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Z2 topological order and topological protection of majorana fermion qubits
AU - Haq, Rukhsan Ul
AU - Kauffman, Louis H.
N1 - Funding Information: Funding: L. H. Kauffman’s work was supported by the Laboratory of Topology and Dynamics, Novosibirsk State University (contract no. 14.Y26.31.0025 with the Ministry of Education and Science of the Russian Federation.) Publisher Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/3
Y1 - 2021/3
N2 - The Kitaev chain model exhibits topological order that manifests as topological degeneracy, Majorana edge modes and Z2 topological invariant of the bulk spectrum. This model can be obtained from a transverse field Ising model(TFIM) using the Jordan–Wigner transformation. TFIM has neither topological degeneracy nor any edge modes. Topological degeneracy associated with topological order is central to topological quantum computation. In this paper, we explore topological protection of the ground state manifold in the case of Majorana fermion models which exhibit Z2 topological order. We show that there are at least two different ways to understand this topological protection of Majorana fermion qubits: one way is based on fermionic mode operators and the other is based on anti-commuting symmetry operators. We also show how these two different ways are related to each other. We provide a very general approach to understanding the topological protection of Majorana fermion qubits in the case of lattice Hamiltonians. We then show how in topological phases in Majorana fermion models gives rise to new braid group representations. So, we give a unifying and broad perspective of topological phases in Majorana fermion models based on anti-commuting symmetry operators and braid group representations of Majorana fermions as anyons.
AB - The Kitaev chain model exhibits topological order that manifests as topological degeneracy, Majorana edge modes and Z2 topological invariant of the bulk spectrum. This model can be obtained from a transverse field Ising model(TFIM) using the Jordan–Wigner transformation. TFIM has neither topological degeneracy nor any edge modes. Topological degeneracy associated with topological order is central to topological quantum computation. In this paper, we explore topological protection of the ground state manifold in the case of Majorana fermion models which exhibit Z2 topological order. We show that there are at least two different ways to understand this topological protection of Majorana fermion qubits: one way is based on fermionic mode operators and the other is based on anti-commuting symmetry operators. We also show how these two different ways are related to each other. We provide a very general approach to understanding the topological protection of Majorana fermion qubits in the case of lattice Hamiltonians. We then show how in topological phases in Majorana fermion models gives rise to new braid group representations. So, we give a unifying and broad perspective of topological phases in Majorana fermion models based on anti-commuting symmetry operators and braid group representations of Majorana fermions as anyons.
KW - Emergent Majorana Modes
KW - Majorana fermion braiding
KW - Majorana fermion models
KW - Topological Protection
UR - http://www.scopus.com/inward/record.url?scp=85102514498&partnerID=8YFLogxK
U2 - 10.3390/condmat6010011
DO - 10.3390/condmat6010011
M3 - Article
AN - SCOPUS:85102514498
VL - 6
SP - 1
EP - 22
JO - Condensed Matter
JF - Condensed Matter
SN - 2410-3896
IS - 1
M1 - 11
ER -
ID: 28257867