If you consider general operators A and B and if you only want to make positive time steps (which is what you usually require when solving parabolic problems), there is an order barrier of 2, i.e., using any kind of splitting, you cannot obtain a rate of convergence higher than two. An elementary proof is given in a recent paper by S. Blanes and F. Casas, http://www.gicas.uji.es/Fernando/MyPapers/2005APNUM.pdf .
However, there are several ways out if you know a little bit more about your problem:
- Assume that you can solve your equations backward in time (which is common for, e.g., Schrödinger equations), then there are many splittings available, see the book "Geometric Numerical Integration" by Hairer, Lubich, and Wanner.
- If your operators generate analytic semigroups, i.e., you can insert complex values for t (typical for parabolic equations), it was recently observed that you can obtain higher order splittings by going into the complex plane. The first articles in that direction are by E. Hansen and A. Ostermann, http://www.maths.lth.se/na/staff/eskil/dataEskil/articles/Complex.pdf , and F. Castella, P. Chartier, S. Descombes, and G. Vilmart. The choice of complex splittings that are "optimal" in some sense is a topic of current research, you can find several papers on the topic on arxiv.
Summing up: If you put in some assumptions on your problem, you can get something, but if not, then order 2 is the maximum.
PS.: I had to take the link to the Castella et al-paper out due to spam prevention, but you can easily find it on google.