If you don't mind creating an extra string:
String zeros = new String(new char[n]).replace((char) 0, '0');
Or more explicit (and probably more efficient):
char[] c = new char[n];
Arrays.fill(c, '0');
String zeros = new String(c);
Performance wise, the Arrays.fill option seems to perform better in most situations, but especially for large strings. Using a StringBuilder is quite slow for large strings but efficient for small ones. Using replace is a nice one liner and performs ok for larger strings, but not as well as filll.
Micro benchmark for different values of n:
Benchmark                       (n)  Mode  Samples        Score         Error  Units
c.a.p.SO26504151.builder          1  avgt        3       29.452 ±       1.849  ns/op
c.a.p.SO26504151.builder         10  avgt        3       51.641 ±      12.426  ns/op
c.a.p.SO26504151.builder       1000  avgt        3     2681.956 ±     336.353  ns/op
c.a.p.SO26504151.builder    1000000  avgt        3  3522995.218 ±  422579.979  ns/op
c.a.p.SO26504151.fill             1  avgt        3       30.255 ±       0.297  ns/op
c.a.p.SO26504151.fill            10  avgt        3       32.638 ±       7.553  ns/op
c.a.p.SO26504151.fill          1000  avgt        3      592.459 ±      91.413  ns/op
c.a.p.SO26504151.fill       1000000  avgt        3   706187.003 ±  152774.601  ns/op
c.a.p.SO26504151.replace          1  avgt        3       44.366 ±       5.153  ns/op
c.a.p.SO26504151.replace         10  avgt        3       51.778 ±       2.959  ns/op
c.a.p.SO26504151.replace       1000  avgt        3     1385.383 ±     289.319  ns/op
c.a.p.SO26504151.replace    1000000  avgt        3  1486335.886 ± 1807239.775  ns/op