PreprintCC BY 4.0arXiv
Fractional Hall Conductance of Laughlin States from a Topological Index
Abstract
We provide a rigorous Laughlin-pump argument that establishes the fractional quantization of the Hall conductance directly from the Laughlin state as a topological index. Our proof uses a recently defined index of a pair of pure states together with an infinite matrix product state analysis that is rigorous on a sufficiently thin cylinder. By virtue of the connection to an index, our result implies, in particular, that Laughlin states are representatives of topologically stable fractional quantum Hall phases.
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BibTeX
@misc{bachmann2026fractional,
title = {{Fractional Hall Conductance of Laughlin States from a Topological Index}},
author = {Sven Bachmann and Severin Schraven and Jacob Shapiro and Simone Warzel},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27767},
eprint = {2608.27767},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27767},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fractional Hall Conductance of Laughlin States from a Topological Index
AU - Sven Bachmann
AU - Severin Schraven
AU - Jacob Shapiro
AU - Simone Warzel
PY - 2026
DA - 2026/08/27
PB - arXiv
DO - 10.48550/arxiv.2608.27767
UR - https://arxiv.org/abs/2608.27767
AB - We provide a rigorous Laughlin-pump argument that establishes the fractional quantization of the Hall conductance directly from the Laughlin state as a topological index. Our proof uses a recently defined index of a pair of pure states together with an infinite matrix product state analysis that is rigorous on a sufficiently thin cylinder. By virtue of the connection to an index, our result implies, in particular, that Laughlin states are representatives of topologically stable fractional quantum Hall phases.
ER -