Bethe-Ansatz and quantum groups: The Light cone lattice approach. 1. Six vertex and SOS models

Jun, 1991
28 pages
Published in:
  • Nucl.Phys.B 374 (1992) 692-719
  • Published: 1992
Report number:
  • PAR-LPTHE-91-32

Citations per year

1992200020082016202302468
Abstract: (Elsevier)
The six-vertex model is solved with fixed boundary conditions (FBC) that guarantee exact SU(2) q invariance on the lattice. The algebra of the Yang-Baxter (YB) and SU(2) q generators turns to close and the transfer matrix is SU(2) q -invariant for FBC. In addition, the infinite spectral parameter limit of the YB generators yields cleanly the SU(2) q generators. The Bethe ansatz states constructed for FBC are shown to be the highest weights of SU(2) q . The light-cone evolution operator for FBC is introduced and shown to follow from the row-to-row FBC transfer matrix with alternating inhomogeneities. This operator is shown to describe the SOS model after an appropriate gauge choice. Using this FBC light-cone approach, the scaling limit of both six-vertex and SOS models easily follows. Finally, the higher level Bethe ansatz equations (describing the physical excitations) are explicitly derived for FBC.
  • quantum group: SU(2)
  • lattice field theory: Bethe ansatz
  • lattice field theory: light cone
  • model: vertex
  • Yang-Baxter equation
  • scaling
  • transfer matrix
  • boundary condition
  • integrability