How can I divorce my husband who no longer lives in the same state and with whom I have no way of contacting?

Court action cannot be taken against a someone without giving them an opportunity to be heard. Therefore, notice must be given to them that a lawsuit has been filed, including a divorce action. And in a situation in which a spouse is missing the law allows for what is caalled a "divorce by publication".
The way it works is that the "petitioner i.e. the filing spouse is required to make a diligent effort to find the "respondent" i.e. the absent spouse. The petititoner will have to present proof to the court that they made every effort to search for the respondent, such as checking with /friends/family/former landlords, the phone book, voting records, the DMV or any other source lthat is likely to lead to the missing spouse's location.
If the petitioner has no success in finding the whereabouts of their spouse, the petitioner will be allowed to serve the repondent by publishing notice of their divorce in a newspaper. The judge will instruct which papers to use. As a general rule, it will be in one that is in the area of the missing spouse's last known location.
In most states, the respondent has between 30-60 days to file an answer after the first day of publication. If they fail to do so within that time, the petitioner can file a request to enter a "default dissolution" of marriage i.e. divorce. Typically it is granted upon the terms and conditions that the petitioner requests although the respondent does have a certain period of time in which they can appeal the divorce/terms.
At this point you might want to consult directly with a divorce attorney in your area. They can best advise further as to specific state law.