Integrability and symmetry of the XXZ model

Cao, Li-Ke, Ke Ke +3 more

Tetsuji Miwa

Pascal Baseilhac, S. Belliard

The non-Abelian symmetries of the half-infinite XXZ spin chain for all possible types of integrable boundary conditions are classified. For each type of boundary conditions, an analog of the Chevalley-type presentation is given for the corresponding symmetry algebra. In particular, two new algebras arise that are, respectively, generated by the symmetry operators of the model with triangular and special Uq(gl2)-invariant integrable boundary conditions.

Márton Borsi, Balázs Pozsgay

Abstract We consider spin chain models with exotic symmetries that change the length of the spin chain. It is known that the XXZ Heisenberg spin chain at the supersymmetric point Δ = − 1 / 2 possesses such a symmetry: it is given by the supersymmetry generators, which change the length of the chain by one unit. We show that volume changing symmetries exist also in other spin chain models, and that they can be constructed using a special tensor network, which is a simple generalization of a Matrix Product Operator (MPO). As examples we consider the folded XXZ model and its perturbations, and also a new hopping model that is defined on constrained Hilbert spaces. We show that the volume changing symmetries are not related to integrability: the symmetries can survive even non-integrable perturbations. We also show that the known supersymmetry generator of the XXZ chain with Δ = − 1 / 2 can also be expressed as a generalized MPO.

Minoru Takahashi

Murray T. Batchelor

The hamiltonian of an asymmetric diffusion process with injection and ejection of particles at the ends of a chain of finite length is known to be relevant to that of the spin-1/2 XXZ chain with integrable boundary terms. However, the inclusion of boundary sources and sinks of particles breaks the arrow-reversal symmetry necessary for solution via the usual Bethe Ansatz approach. Developments in solving the model in the absence of arrow-reversal symmetry are discussed.