Geometric test for topological states of matter
Autor: | S. Klevtsov, D. Zvonkine |
---|---|
Přispěvatelé: | Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ) |
Rok vydání: | 2021 |
Předmět: |
High Energy Physics - Theory
General Physics and Astronomy FOS: Physical sciences 01 natural sciences 010305 fluids & plasmas topological Condensed Matter - Strongly Correlated Electrons [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] 0103 physical sciences surface 010306 general physics Mathematical Physics Condensed Matter::Quantum Gases Strongly Correlated Electrons (cond-mat.str-el) [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] Hilbert space Aharonov-Bohm effect Mathematical Physics (math-ph) Condensed Matter::Mesoscopic Systems and Quantum Hall Effect [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] flux High Energy Physics - Theory (hep-th) fractional many-body problem slope quantization |
Zdroj: | Physical Review Letters Physical Review Letters, American Physical Society, In press |
ISSN: | 0031-9007 1079-7114 |
DOI: | 10.48550/arxiv.2105.00989 |
Popis: | We generalize the flux insertion argument due to Laughlin, Niu-Thouless-Tao-Wu, and Avron-Seiler-Zograf to the case of fractional quantum Hall states on a higher-genus surface. We propose this setting as a test to characterise the robustness, or topologicity, of the quantum state of matter and apply our test to the Laughlin states. Laughlin states form a vector bundle, the Laughlin bundle, over the Jacobian - the space of Aharonov-Bohm fluxes through the holes of the surface. The rank of the Laughlin bundle is the degeneracy of Laughlin states or, in presence of quasiholes, the dimension of the corresponding full many-body Hilbert space; its slope, which is the first Chern class divided by the rank, is the Hall conductance. We compute the rank and all the Chern classes of Laughlin bundles for any genus and any number of quasiholes, settling, in particular, the Wen-Niu conjecture. Then we show that Laughlin bundles with non-localized quasiholes are not projectively flat and that the Hall current is precisely quantized only for the states with localized quasiholes. Hence our test distinguishes these states from the full many-body Hilbert space. Comment: 6 pages |
Databáze: | OpenAIRE |
Externí odkaz: |