Spontaneous orientation of a quantum lattice string

Using exact diagonalization and quantum Monte-Carlo techniques we study a quantum lattice string model introduced as a model for a single cuprate struipe. We focus on the ground state properties of the string. Our results shows that, in the physically relevant region of the parameter space, a zero temperature spontaneous symmetry breaking occures. The string spontaneously orients itself along one direction in space and become directed. We introduce an order parameter for the directedness and show that at zero temperature this order parameter reaches its saturation value.