Can a single Soldier living in the barracks file "head of household" for taxes?

No, you cannot file as Head of Household.

To file as HoH, you must pay more than half of the cost of maintaining a home and a Qualifying Person must live in the home. A Qualifying Person can be your minor child who lived with you for more than half of the year that you can claim as your dependent or certain other closely related persons such as an elderly parent that you do claim as your dependent.

The child's mother can give you a Form 8332 allowing you to claim the child's exemption and the Child Tax Credit. The mother retains the right to file as HoH, claim the EIC, and claim the Child & Dependent Care Credit if otherwise eligible. Regardless of what the court order states, without the Form 8332 attached to your return, you may NOT claim your child since she did not live in your home for more than half of 2013.

Edit: Just to correct a major error by NA -- the fact that the taxpayers pay for your housing is irrelevant. If you lived in MFH and your daughter lived with you for more than half of the year, you absolutely could file as HoH. The housing allowance that you surrender in order to occupy MFH covers 100% of the cost of maintaining the home (other than possibly renter's insurance which is peanuts on most military installations) so you easily meet the more than 50% test.

You can't claim HoH, the related dependent has to live with you. Court order gives you the exemption ONLY, not the HoH filing, or anything else, that stays with child's mom.

Bottom line, you cannot file HoH.

Head of Household for IRS purposes requires that you have a qualifying dependent who lives with you.

The form 8332 will NOT make you eligible, it just lets you claim your daughter's exemption and child tax credit. It does NOT make you eligible for EIC, child care or HOH.

Even if your child lived with you, you are NOT paying more than half if the taxpayer's are picking up the tab.

No. First, the household has to be more than one person, and they have to be living together. You have to have a dependent who either (a) is your parent, or (b) lives with you. Claiming someone who doesn't live with you (except your parent) doesn't help.

sure, why not?