Indexes may also be used to enforce uniqueness of a column's value,
   or the uniqueness of the combined values of more than one column.
CREATE UNIQUE INDEX name ON table (column [, ...]);
   Currently, only B-tree indexes can be declared unique.
  
   When an index is declared unique, multiple table rows with equal
   indexed values will not be allowed.  NULL values are not considered
   equal.
  
   PostgreSQL automatically creates unique
   indexes when a table is declared with a unique constraint or a
   primary key, on the columns that make up the primary key or unique
   columns (a multicolumn index, if appropriate), to enforce that
   constraint.  A unique index can be added to a table at any later
   time, to add a unique constraint.
  
Note:     The preferred way to add a unique constraint to a table is
    ALTER TABLE ... ADD CONSTRAINT.  The use of
    indexes to enforce unique constraints could be considered an
    implementation detail that should not be accessed directly.