Can I get compensation from by the apartment management for the burglury happened at my apartment?

There are two limitations on this kind of claim. First, when the defendant (in this case, your landlord) didn't directly cause the loss -- in this case, the loss was the result of the supervening criminal act of an unknown third party -- there are liability problems in our system, since, as a general matter, the legal system relies on causation as a means of proving duty. Second, you shoukd read your lease and see if the landlord's liability for third-party acts has been waived or excused; often that is the case. There are some newer cases that impose duty on a landlord to provide certain security measures under circumstances where the landlord knew, or reasonably should have known, that crime was likely to result in the neighborhood. But in general, the prospects are not great for such a claim, and it will not be possible to find an attorney who can prosecute this kind of matter cost-effectively. You should consider small claims, where you can be self-represented, as an option. Remember that in order to prevail you will need to show something more than that the landlord left materials for you that advertised your absence. Good luck with it.