Microscopic diagnosis of universal geometric responses in fractional quantum Hall liquids
Abstract
Topological quantum liquids contain internal degrees of freedom that are coupled to geometric response. Yet, an explicit and microscopic identification of the geometric response remains difficult. Here, taking notable fractional quantum Hall (FQH) states as typical examples, we systematically investigate a promising protocol—the Dehn-twist deformation on the torus geometry—to probe the geometric response of correlated topological states and establish the relation between such response and universal properties of pertinent states. Based on analytical derivations and numerical simulations, we find that the geometry-induced Berry phase encodes features for a broad class of FQH states at the Laughlin, hierarchy, Halperin and non-Abelian Moore-Read fillings. Our findings conclusively demonstrate that the adiabatic Dehn-twist deformation can faithfully capture rich geometric and topological information, including the Hall viscosity and topological spin of the pertinent FQH state and the chiral central charge of the underlying edge conformal field theory. Our approach provides a powerful way to reveal topological orders of generic FQH states and address previously open questions.
- Authors:
-
[2];
- Westlake Univ., Hangzhou (China)
- Zhejiang Univ., Hangzhou (China)
- California State University, Northridge (CSUN), CA (United States)
- Princeton Univ., NJ (United States)
- Publication Date:
- Research Org.:
- Princeton Univ., NJ (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1850792
- Grant/Contract Number:
- SC0002140
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 103; Journal Issue: 8; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics; Fractional quantum Hall effect; Geometric & topological phases; Exact diagonalization; Non-Abelian models
Citation Formats
Hu, Liangdong, Liu, Zhao, Sheng, D. N., Haldane, F. D. M., and Zhu, W. Microscopic diagnosis of universal geometric responses in fractional quantum Hall liquids. United States: N. p., 2022.
Web. doi:10.1103/physrevb.103.085103.
Hu, Liangdong, Liu, Zhao, Sheng, D. N., Haldane, F. D. M., & Zhu, W. Microscopic diagnosis of universal geometric responses in fractional quantum Hall liquids. United States. https://doi.org/10.1103/physrevb.103.085103
Hu, Liangdong, Liu, Zhao, Sheng, D. N., Haldane, F. D. M., and Zhu, W. Tue .
"Microscopic diagnosis of universal geometric responses in fractional quantum Hall liquids". United States. https://doi.org/10.1103/physrevb.103.085103. https://www.osti.gov/servlets/purl/1850792.
@article{osti_1850792,
title = {Microscopic diagnosis of universal geometric responses in fractional quantum Hall liquids},
author = {Hu, Liangdong and Liu, Zhao and Sheng, D. N. and Haldane, F. D. M. and Zhu, W.},
abstractNote = {Topological quantum liquids contain internal degrees of freedom that are coupled to geometric response. Yet, an explicit and microscopic identification of the geometric response remains difficult. Here, taking notable fractional quantum Hall (FQH) states as typical examples, we systematically investigate a promising protocol—the Dehn-twist deformation on the torus geometry—to probe the geometric response of correlated topological states and establish the relation between such response and universal properties of pertinent states. Based on analytical derivations and numerical simulations, we find that the geometry-induced Berry phase encodes features for a broad class of FQH states at the Laughlin, hierarchy, Halperin and non-Abelian Moore-Read fillings. Our findings conclusively demonstrate that the adiabatic Dehn-twist deformation can faithfully capture rich geometric and topological information, including the Hall viscosity and topological spin of the pertinent FQH state and the chiral central charge of the underlying edge conformal field theory. Our approach provides a powerful way to reveal topological orders of generic FQH states and address previously open questions.},
doi = {10.1103/physrevb.103.085103},
journal = {Physical Review. B},
number = 8,
volume = 103,
place = {United States},
year = {Tue Feb 01 00:00:00 EST 2022},
month = {Tue Feb 01 00:00:00 EST 2022}
}
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