Critical Exponents of the Chiral Potts Model from Conformal Field Theory

The $Z_N$-invariant chiral Potts model is considered as a perturbation of a $Z_N$ conformal field theory. In the self-dual case the renormalization group equations become simple, and yield critical exponents and anisotropic scaling which agree with exact results for the super-integrable lattice models. Although the continuum theory is not Lorentz invariant, it respects a novel type of space-time symmetry which allows for the observed spontaneous breaking of translational symmetry in the ground state. The continuum theory is shown to possess an infinite number of conserved charges on the self-dual line, which remain conserved when the theory is perturbed by the energy operator.Comment: 15 page

Direction dependent free energy singularity of the asymmetric six-vertex model

The transition from the ordered commensurate phase to the incommensurate gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the external fields $(h,v)$. In the $(h,v)$ plane, the phase boundary is approached along straight lines $\delta v=k \delta h$, where $(\delta h,\delta v)$ measures the displacement from the phase boundary. It is found that the free energy singularity displays the exponent 3/2 typical of the Pokrovski-Talapov transition $\delta f \sim const (\delta h)^{3/2}$ for any direction other than the tangential one. In the latter case $\delta f$ shows a discontinuity in the third derivative.Comment: 18 pages, Latex, 1 figure, minor corrections and two references change

Notions of controllability for quantum mechanical systems

In this paper, we define four different notions of controllability of physical interest for multilevel quantum mechanical systems. These notions involve the possibility of driving the evolution operator as well as the state of the system. We establish the connections among these different notions as well as methods to verify controllability. The paper also contains results on the relation between the controllability in arbitrary small time of a system varying on a compact transformation Lie group and the corresponding system on the associated homogeneous space. As an application, we prove that, for the system of two interacting spin 1/2 particles, not every state transfer can be obtained in arbitrary small time.Comment: Replaced by a new version which contains the proof