Quantum integrable 1D anyonic models: construction through braided Yang-Baxter equation

DOI10.3842/SIGMA.2010.080zbMATH Open1219.81151arXiv1005.4603MaRDI QIDQ542699

Anjan Kundu

Publication date: 17 June 2011

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Abstract: Applying braided Yang-Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed. Along with known models we discover novel lattice anyonic and $q$-anyonic models as well as nonlinear Schr"odinger equation (NLS) and the derivative NLS quantum field models involving anyonic operators, $N$-particle sectors of which yield the well known anyon gases, interacting through $delta$ and derivative $delta$-function potentials.

Full work available at URL: https://arxiv.org/abs/1005.4603

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zbMATH Keywords

algebraic Bethe ansatzquantum integrability1D anyonic and \(q\)-anyonic lattice modelsanyonic NLS and derivative NLS field modelsbraided YBEnonultralocal model

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Statistical mechanics of crystals (82D25) NLS equations (nonlinear Schrödinger equations) (35Q55) Exactly solvable models; Bethe ansatz (82B23) Groups and algebras in quantum theory and relations with integrable systems (81R12) Yang-Baxter equations (16T25)

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