With PostgreSQL there are a number of date/time functions available, see here.
In your example, you could use:
SELECT * FROM myTable WHERE date_trunc('day', dt) = 'YYYY-MM-DD';
If you are running this query regularly, it is possible to create an index using the date_trunc
function as well:
CREATE INDEX date_trunc_dt_idx ON myTable ( date_trunc('day', dt) );
One advantage of this is there is some more flexibility with timezones if required, for example:
CREATE INDEX date_trunc_dt_idx ON myTable ( date_trunc('day', dt at time zone 'Australia/Sydney') );
SELECT * FROM myTable WHERE date_trunc('day', dt at time zone 'Australia/Sydney') = 'YYYY-MM-DD';