Is it possible to go by public transport from the centre of Xian to the terracotta army?

Yes, the transportation is convenient.
You can go to the East Square of Main Railway Station first. Then you can find many tourist buses no.line 5 that can take you to the scenic spot directly.
The bus schedules are from 07:00 ~19:00 with an interval of about 15 minutes. It takes around 40 mins. And the ticket fare is CNY 7 per person.