Exact solution of the one-dimensional isotropic Heisenberg chain with arbitrary spins S

New integrable structures in large-NQCD

“…Remarkably, the spin chain (18) is integrable [40,41,42,15] and the Hamiltonian can be diagonalized by Bethe ansatz [43,44]! The Bethe equations constitute a set of algebraic equations for rapidities of elementary excitations on the lattice:…”

“…The real vacuum is a Lorentz scalar and has negative anomalous dimension (as an effect of the asymptotic freedom). In the thermodynamic limit of large L [43,44]:…”

Exact spectrum of the spin-s Heisenberg chain with generic non-diagonal boundaries

“…The completeness of the Bethe ansatz solution was already studied in [56-59, 73, 77]. Here we provide numerical evidence for the s = 1 case, which corresponds to the isotropic Fateev-Zamolodchikov (or Takhtajan-Babujian) model [14,[22][23][24] with general non-diagonal boundary terms. In terms of the basis {|l |l = 1, 0, −1} given by…”

“…The high spin models with periodic [14][15][16][17][18][19][22][23][24] and diagonal [69][70][71] boundaries have been extensively studied. Even the most general integrable boundary condition (corresponding to the non-diagonal reflection matrix) for the spin-1 model has been known for many years [72], the exact solutions of the models with non-diagonal boundaries were known only for some special cases such as the boundary parameters obeying some constraint [52] or the crossing parameter taking some special value (e.g., roots of unity) [53,54].…”

“…Its generalization to arbitrary s cases was subsequently constructed via the fusion techniques [15][16][17][18][19] based on the fundamental s = 1 2 representations of the Yang-Baxter equation [20,21]. Those observations allow one to diagonalize the models with periodic boundary conditions in the framework of algebraic Bethe ansatz method (for example, see [22][23][24]). On the other hand, the discovery of the boundary Yang-Baxter equation or the reflection equation [25,26] directly stimulated the studies on the exact solutions of the quantum integrable models with boundary fields.…”