  Integrable quantum field models are known to exist mostly in one
space-dimension. Exploiting the concept of multi-time in integrable systems and
a Lax matrix of higher scaling order, we construct a novel quantum field model
in quasi-two dimensions involving interacting fields. The Yang-Baxter
integrability is proved for the model by finding a new kind of commutation rule
for its basic fields, representing nonstandard scalar fields along the
transverse direction. In spite of a close link with the quantum Landau-Lifshitz
equation, the present model differs widely from it, in its content and the
result obtained. Using further the algebraic Bethe ansatz we solve exactly the
eigenvalue problem of this quantum field model for all its higher conserved
operators. The idea presented here should instigate the construction of a novel
class of integrable field and lattice models and exploration of a new type of
underlying algebras.
