This article is cited in 4 papers

Quantum Integrable 1D anyonic Models: Construction through Braided Yang–Baxter Equation

Anjan Kundu

Theory Group \& CAMCS, Saha Institute of Nuclear Physics, Calcutta, India

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 Schrödinger 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.

Keywords: nonultralocal model; braided YBE; quantum integrability; 1D anyonic and $q$-anyonic lattice models; anyonic NLS and derivative NLS field models; algebraic Bethe ansatz.

MSC: 16T25; 20F36; 81R12

Received: May 25, 2010; in final form October 3, 2010; Published online October 9, 2010

Language: English

DOI: 10.3842/SIGMA.2010.080

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ArXiv: 1005.4603