Break the lease--likely not. But you do have a couple options.
You've done everthing you are supposed to--notification in writing, housing authority documentation (I am assuming you are in a complex and therefore your tenancy falls under the Virginia Residential Landlord Tenant Act (VRLTA)). http://www.dhcd.virginia.gov/HomelessnesstoHomeownership/PDFs/Landlord_Tenant_Handbook.pdf
Your options as I see it:
1. You could sue (in small claims, no lawyers) for breach of contract on grounds the LL did not provide you a fit place for habitation. Its not a slam dunk--some courts have found roaches a safety and health hazard that rises to the level of material breach of contract, others have not--in part it depends on the degree of documented infestation. The VRLTA makes no provision about whether roaches are a safety hazard, only that tenant's must inform landlords and tenants must take reasonable steps themselves too.
2. You could file a 'tenant's assertion' in General District Court. You don't need a lawyer, the clerks or library staff in the law library can give you the forms--they are also avaliable from the court, on-line for free. Pay your rent into an escrow account established by the court (costs $56 as I recall to set it up, $12 to serve notice on the LL) until LL eradicates--then the court determines if LL gets all or some of the accrrued rent in the escrow account. If only some goes to the LL, you get the balance back--sort of a rent abatement for your troubles.
If it were me I would write a letter to LL (certified, RRR) in which I documented the saga and offer that I am holding the LL in breach of contract and will sue if LL fails to act to eradicate the roach den in the building within five days. (it may likely require LL treat all the apartments in the building).
If LL failed to act, I would file the tenant's assertion and divert myr money to the court and away from the LL.
I doubt a court would withold all the money from the LL in the end, but it does provide some leverage and the court might return a portion of the rent money.
READ THIS BEFORE CALLING OR EMAILING ME: I am licensed to practice before the state and federal courts in Virginia. Addressing your issue does not create an attorney-client relationship and I AM providing you educational information NOT legal advice. You should speak with an attorney to whom you have provided all the facts, before you take steps that may impact your legal rights. I am not obligated to answer subsequent emails or phone calls unless you have hired me. I wish you the best of luck with your situation.