Is the Latent Dirichlet Allocation topic posterior multimodal?

In fitting the Latent Dirichlet Allocation with collapsed Gibbs sampling one builds a sampled approximation to the topic posterior distribution, $P(z|w)$ and use that to calculate the topic and word probabilities for each document.

Is this posterior distribution uni-modal? Or are there several topic configurations that give rise to the same posterior probability (and hence different, but equally likely topic probabilities for each document)?