Fractional quantum numbers via complex orbifolds

TY - JOUR

T1 - Fractional quantum numbers via complex orbifolds

AU - Mathai, Varghese

AU - Wilkin, Graeme Peter Desmond

N1 - © Springer Nature B.V. 2019. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

PY - 2020/10/17

Y1 - 2020/10/17

N2 - This paper studies both the conductance and charge transport on 2D orbifolds in a strong magnetic field. We consider a family of Landau Hamiltonians on a complex, compact 2D orbifold Y that are parametrised by the Jacobian torus J(Y) of Y. We calculate the degree of the associated stable holomorphic spectral orbibundles when the magnetic field B is large and obtain fractional quantum numbers as the conductance and a refined analysis also gives the charge transport. A key tool studied here is a nontrivial generalisation of the Nahm transform to 2D orbifolds.

AB - This paper studies both the conductance and charge transport on 2D orbifolds in a strong magnetic field. We consider a family of Landau Hamiltonians on a complex, compact 2D orbifold Y that are parametrised by the Jacobian torus J(Y) of Y. We calculate the degree of the associated stable holomorphic spectral orbibundles when the magnetic field B is large and obtain fractional quantum numbers as the conductance and a refined analysis also gives the charge transport. A key tool studied here is a nontrivial generalisation of the Nahm transform to 2D orbifolds.

KW - Fractional quantum numbers

KW - Riemann orbifolds

KW - Holomorphic orbifolds

KW - Orbifold Nahm transform

UR - http://www.scopus.com/inward/record.url?scp=85068350942&partnerID=8YFLogxK

U2 - 10.1007/s11005-019-01190-y

DO - 10.1007/s11005-019-01190-y

M3 - Article

SN - 1573-0530

VL - 109

SP - 2473

EP - 2484

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 11

ER -