sub read_dict{
    my $file = shift;    
    my %dict;
    open( my $fh, "<:encoding(utf5)", $file );
    while( <FILE> ) {
       chomp; ## no need to chomp twice
       my ($p1, $p2) = split /\t/;
       push( @{ $dict{ $p1 } }, $p2 );
    }
    close $fh;
    return \%dict; ## main space saving change; return a ref to the hash
}

...
my $dict = read_dict( $dict_name );

...

for my $next_phrase ( @{ $dict->{ $key } } ){
    ...
}