To file as head of household when you are married, you must have lived apart from your spouse for all of the second half of 2018, AND provide care in your home for a qualifying dependent, AND pay more than half the cost of maintaining that home.
In your question, you didn’t mention a qualifying dependent.
For living together or apart, what counts is where you and your spouse actually lived. If you lived in the same apartment but he was not on the lease, you did not live apart. If you are playing games with section 8, don’t also play games with the IRS.
For the question of whether you paid more than half the cost of maintaining your home, you have to consider all the other sources of support you had. If you are paying less than fair market value for your apartment because of government assistance, that counts as support provided by the government. If your spouse gives you assistance, or if you receive food stamps or welfare, or other government benefits, or assistance from other family members, that all counts as support not provided by you. You must pay more for your housing than all the other sources of support added together.
