You can use your existing XT crank. If you have a couple of bb laying around with different spindle lenghts you can play around with the chainline. A frame with vertical dropouts to set up a single speed without a chain tensioner is difficult. You have to make sure that your front ring and rear cog ratio is exact to the chainstay length in relation to the number of chain links.
On my wifes bike for example I missed by a HALF a link! Made all the difference though I had to use a tensioner.