The exact correspondence between conserved quantities of a periodic box-ball system and string solutions of the Bethe ansatz equations. (English) Zbl 1111.82014
Summary: We investigate the link between a periodic box-ball system (PBBS) and a solvable lattice model. Introducing a PBBS with an integer parameter corresponding to the dimensionality of the auxiliary space for the lattice model, we prove an important relationship between the conserved quantities of states of the PBBS and eigenvectors constructed through the string hypothesis.
MSC:
| 82B23 | Exactly solvable models; Bethe ansatz |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
References:
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