Protracted withdrawals from benzodiazepine can last for weeks, considering you only took 1 mg daily for 4 weeks I imagine the symptoms won't be extreme but mild symptoms might last for up to 4 weeks (mainly relating to cognitive function). Psychological dependence is much harder to determine, since it relates to why you use the substance (what relief did it provide you?).
If you are suffering from anxiety you are more likely to experience cravings for the xanax because you know it will chill you out. Best thing for you would be to get some exercise, drink plenty of water, eat a hearty diet and drink hot beverages. I find that diphenhydramine (Benadryl) helps if you are having trouble sleep, or feel anxious.