Integrable Models From Twisted Half Loop Algebras

Abstract

This paper is devoted to the construction of new integrable quantum mechanical models based on certain subalgebras of the half loop algebra of gl(N). Various results about these subalgebras are proven by presenting them in the notation of the St Petersburg school. These results are then used to demonstrate the integrability, and find the symmetries, of two types of physical system: twisted Gaudin magnets, and Calogero-type models of particles on several half-lines meeting at a point.

22 pages, 1 figure, Introduction improved, References added

References in corpus (17)

• How Algebraic Bethe Ansatz works for integrable model
• Exchange Operator Formalism for Integrable Systems of Particles
• Kirchhoff's Rule for Quantum Wires
• Exactly solvable Richardson-Gaudin models for many-body quantum systems
• Yang-Baxter equation in spin chains with long range interactions
• Explicit Solution to the N-Body Calogero Problem
• Hamiltonian systems of Calogero type and two dimensional Yang-Mills theory
• Classically integrable boundary conditions for affine Toda field theories
• Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins
• Explicit Relation of Quantum Hall Effect and Calogero-Sutherland Model
• Quantum spin chain with "soliton non-preserving" boundary conditions
• Separation of Variables in BC-type Gaudin Magnet
• New non-diagonal solutions to the $a_n^{(1)}$ boundary Yang-Baxter equation
• Analytical Bethe Ansatz for open spin chains with soliton non preserving boundary conditions
• Background field boundary conditions for affine Toda field theories
• Rational Lax operators and their quantization
• New spin generalisation for long range interaction models

Cited by in corpus (9)

• Integrable boundary conditions and modified Lax equations
• Cyclotomic Gaudin models: construction and Bethe ansatz
• FRT presentation of the Onsager algebras
• Cyclotomic Gaudin models with irregular singularities
• Sutherland Models for Complex Reflection Groups
• Classical $N$-Reflection Equation and Gaudin Models
• Symmetries of Spin Calogero Models
• $({\mathfrak{gl}}_M,{\mathfrak{gl}}_N)$-Dualities in Gaudin Models with Irregular Singularities
• Populations of Solutions to Cyclotomic Bethe Equations