Integrability of the Quantum XXZ Hamiltonian

Andreas Klümper

M. C. Cambiaggio, Alejandro M. F. Rivas, Marcos Saraceno

Andrei G. Bytsko

Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to 32 are given. Relations between Hamiltonians for some Uq(sl2)-symmetric and U(1)-symmetric universal r-matrices are studied; their properties are investigated. A certain modification of the higher spin periodic chain Hamiltonian is shown to be an integrable Uq(sl2)-symmetric Hamiltonian for an open chain.

Nikolai A. Sinitsyn, Emil A. Yuzbashyan, Vladimir Chernyak +2 more

Andrei Bytsko

Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to 3/2 are given. Relations between Hamiltonians for some U_q(sl_2)-symmetric and U(1)-symmetric universal r-matrices are studied; their properties are investigated. A connection with open chain Hamiltonians is discussed.

Gus Schrader

In this paper we analyze the classical XXZ spin chain with reflecting boundaries. We exhibit a system of log-canonical coordinates on the phase space generalizing Sklyanin's separation of variables for the periodic XXZ chain, and use these coordinates to construct action-angle variables for the system. We also integrate the flows of the reflection Hamiltonians explicitly in terms of Riemann theta functions. Central to our analysis is the algebraic integrability of the model.