How to discard trash topics from topic models?
I assume you have inspected your topic-by-word matrix, and that is why you say you have 'trash' topics.  If no words are strongly associated with a given topic, it may not be a useful topic.  If you find many of these, you can re-run the experiment with fewer topics.  

If instead there are words strongly associated with these topics, you just don't see the cohesive meaning behind the words associated with the topic, then these are not exactly "trash" topics.  They are still capturing the latent structure of the data, it just isn't something easily deemed a "topic" in the traditional sense of the word.

Another thing to remember is that the hyperparameters also control the shape of your resulting distributions.  This answer does a great job explaining alpha and beta.