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Fermion doubling in condensed matter physics : simulating a weyl fermion on a lattice Kapoor, Samarth
Abstract
It is complicated to promote a continuum quantum theory with fermions to a lattice. This problem is caused by an unexpected appearance of extra states in the lattice theory - the fermion doubling problem. Nielsen and Ninomiya proved in 1981 that under certain conditions, it is actually impossible to find a lattice that simulates a single Weyl fermion. We realize that one of the crucial assumptions in their proof is the conservation of electric charge - a condition which is not held in topological superconductors. A common toy model for topological superconductors is the one-dimensional Kitaev wire. Thus, we propose a similar two-band three-dimensional lattice that has a single Weyl fermion in the low-energy. We find this effective theory by combining the degrees of freedom around the nodal points and then integrating out the extra degrees of freedom using the Schrieffer-Wolff transformation.
Item Metadata
Title |
Fermion doubling in condensed matter physics : simulating a weyl fermion on a lattice
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Creator | |
Supervisor | |
Publisher |
University of British Columbia
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Date Issued |
2022
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Description |
It is complicated to promote a continuum quantum theory with fermions to a lattice. This problem is caused by an unexpected appearance of extra states in the lattice theory - the fermion doubling problem. Nielsen and Ninomiya proved in 1981 that under certain conditions, it is actually impossible to find a lattice that simulates a single Weyl fermion. We realize that one of the crucial assumptions in their proof is the conservation of electric charge - a condition which is not held in topological superconductors. A common toy model for topological superconductors is the one-dimensional Kitaev wire. Thus, we propose a similar two-band three-dimensional lattice that has a single Weyl fermion in the low-energy. We find this effective theory by combining the degrees of freedom around the nodal points and then integrating out the extra degrees of freedom using the Schrieffer-Wolff transformation.
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Genre | |
Type | |
Language |
eng
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Date Available |
2022-09-06
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution 4.0 International
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DOI |
10.14288/1.0418612
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2022-11
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Campus | |
Scholarly Level |
Graduate
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution 4.0 International