J. Dittrich

CZ-250 68 ˇ Reˇz, Czech Republic
Institute of Nuclear Physics, ASCR


Dittrich J., Inozemtsev V. I.
We consider the problem of finding integrals of motion for quantum elliptic Calogero–Moser systems with arbitrary number of particles extended by introducing spinexchange interaction. By direct calculation, after making certain ansatz, we found first two integrals — quite probably, lowest nontrivial members of the whole commutative ring. This result might be considered as the first step in constructing this ring of the operators which commute with the Hamiltonian of the model.
Keywords: quantum elliptic spin systems, transpositions, integrability
Citation: Dittrich J., Inozemtsev V. I.,  Towards the Proof of Complete Integrability of Quantum Elliptic Many-body Systems with Spin Degrees of Freedom, Regular and Chaotic Dynamics, 2009, vol. 14, no. 2, pp. 218-222
Dittrich J., Inozemtsev V. I.
We prove the commutativity of the first two nontrivial integrals of motion for quantum spin chains with elliptic form of the exchange interaction. We also show their liner independence for the number of spins larger than 4. As a byproduct, we obtained several identities between elliptic Weierstrass functions of three and four arguments.
Keywords: quantum elliptic spin chains, transpositions, integrability
Citation: Dittrich J., Inozemtsev V. I.,  The Commutativity of Integrals of Motion for Quantum Spin Chains and Elliptic Functions Identities, Regular and Chaotic Dynamics, 2008, vol. 13, no. 1, pp. 19-26

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