I am trying to run DMRG for the half-filled 4x4 Hubbard using Alps 1.3b and am getting energies which are substantially below the exact value. Granted, the jobs haven't finished, but all my (limited) knowledge of DMRG suggests that the energy will never drop below the exact value during any intermediate point in the calculation.
Hopefully someone can tell me what I am doing wrong with my input file or how my thinking is incorrect. I am confused that it got below E=-16 when the exact result is around E=-13.
Thanks,
Jeff
hubbard.parm: ========================================================= SWEEPS=10 MAXSTATES=1000 MODEL="fermion Hubbard" LATTICE_LIBRARY="/home/jeff/ALPS/lib/xml/lattices.xml" MODEL_LIBRARY="/home/jeff/ALPS/lib/xml/models.xml" CONSERVED_QUANTUMNUMBERS="Nup,Ndown" LATTICE="square lattice" {L=4;Nup_total=8; Ndown_total=8; t=1; U=4} =========================================================
This is how far I ran it before I killed it:
grep ITER *log
... ... ... WARMUP LEFT-TO-RIGHT ITERATION 12 ... ... ... WARMUP RIGHT-TO-LEFT ITERATION 12 ... ... ... WARMUP LEFT-TO-RIGHT ITERATION 12 ... RIGHT-TO-LEFT ITERATION 1 ITER = 1 ENTROPY = 1.00071007161 RIGHT-TO-LEFT ITERATION 2 ITER = 2 ENTROPY = 1.18324332788 RIGHT-TO-LEFT ITERATION 3 ITER = 3 ENTROPY = 1.24380103133 RIGHT-TO-LEFT ITERATION 4 ITER = 4 ENTROPY = 1.35051135715
And this is is where the energy was:
grep ener *log
... ... ... Iter = 2 Ener = -6.9064039895 Iter = 3 Ener = -9.65658596065 Iter = 4 Ener = -12.2462553335 Iter = 5 Ener = -13.9342133195 Iter = 6 Ener = -15.0550663096 Iter = 7 Ener = -15.6408884632 Iter = 8 Ener = -15.9408122129 Iter = 9 Ener = -16.1180047556
The exact result is -13.621854821 and Xiang's momentum space DMRG result is -13.571 (PRB 1996).