Abstract

The quantized Hall conductivity of integer and fractional quantum Hall (IQH and FQH) states is directly related to a topological invariant, the many-body Chern number. The conventional calculation of this invariant in interacting systems requires a family of many-body wave functions parameterized by twist angles to calculate the Berry curvature. In this paper, we demonstrate how to extract the Chern number given a single many-body wave function, without knowledge of the Hamiltonian. For FQH states, our method requires one additional integer invariant as input: the number of 2 pi flux quanta, s, that must be inserted to obtain a topologically trivial excitation. As we discuss, s can be obtained in principle from the degenerate set of ground state wave functions on the torus, without knowledge of the Hamiltonian. We perform extensive numerical simulations involving IQH and FQH states to validate these methods.

Publication Details
Publication Type
Journal Article
Year of Publication
2021
Volume
103
ISSN Number
2469-9950
DOI
10.1103/PhysRevB.103.075102
Journal
Phys. Rev. B
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Contributors
Date Published
FEB 1