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.
Read the upstream documentation. For corrections, first check the current version.