Dear Mr Troyer,
Thank you for your answer. I can agree with you, when we talking about 16 fermions on 32-sites lattice. But I am still confused about one- (or two) particle case. As I understood, regardless of particle number, program builds the matrix dxd (where d is the dimension of the Hilbert space) due to the number of sites. Am I right? Or is it true only for the special case N_total=1? What about N_total=2,3?
Moreover, when I did ED on the other model, and I overestimated the computer capacities, there was an error message (I can't remember what exactly it said), and when I try to make ED on 32-sites graph, with one particle on it there are no errors at all. So why there is no message?
Thank you very much! Volodymyr Derzhko
Dear Volodymyr,
The Hilbert space size for 8 up and 8 down particles in 32 sites is about 10^14 elements. To store the matrix you will thus need 10^31 bytes of memory, or about 10^16 Petabyte, 16 orders of magnitude beyond the memory of the biggest supercomputer in the world. The scaling is exponential.
Matthias