Stripe ansätze from exactly solved models

Using the Boltzmann weights of classical statistical-mechanics vertex models we define a new class of tensor product Ansätze for two-dimensional quantum-lattice systems, characterized by a strong anisotropy, which gives rise to stripelike structures. In the case of the six-vertex model we compute exactly, in the thermodynamic limit, the norm of the Ansatz, and other observables. Employing this Ansatz we study the phase diagram of a Hamiltonian given by the sum of XXZ Hamiltonians along the legs coupled by an Ising term. Finally, we suggest a connection between the six- and eight-vertex anisotropic tensor-product Ansätze, and their associated Hamiltonians, with the smectic-stripe phases recently discussed in the literature.