Dear All I am trying to compute low energy eigenstates of a small L=10 system of spin-1/2 nodes using the DMRG, implemented as mps_optim to compute a ground state and a first excited state for a cetrain model (model.xml pasted below). Unfortunately what i get is two states, but the state returned as a ground state (numer „0“) as a greater energy then the excited state. More specifically I compute the state twice: using NUMBER_EIGENVALUES=1 (then the gs energy is -4) and NUMBER_EIGENVALUES=2 (then the gs energy is -4 and excited state’s energy is -5 (which is is fact the ground state’s energy).
the Fulldiag code returns correct (verified by fulldiag of my own) eigenvalues.
The alps-dmrg does not converge in reasonable number of sweeps. What is worse it returns energy of order of -18, so that is significantly below the ground state energy. Does the alps-dmrg support the hamiltonian that I have wrote at all? FINAL SWEEP - LAST ITERATION NUMBER OF STATES: 16 2 2 16 1024 E0 = -17.4530961018 E0 = -8.52509624929 EXCITED OVERLAP(0) = 3.07571832172e-06 E(1) = -8.52509624929 GAP(1) = -17.4530961018 -8.52509624929 8.92799985252 ITER = 4 ENTROPY = 2.62675527051
DMRG as any minimization routine is subject to „local minimum“ problem, but I have never seen it to fail so dramatically. I had the thought that the key may be the following line in the ouput: "This binary contains symmetries: nu1, "
but I have set nothing like „N_total=10“. Just to be sure I have redefined „spin“ basis to a new „spinc“ from which I have removed the „constraint" metatag.
TO sum up I have following issues/questions: - matter of convergence of mps_optimize - why alps-dmrg returns significantly lower energy than fulldiag on a small exemplary system? - is it some sort of constraints ? I do not want to use any conservation laws. W would like to do a brute DMRG without any good quantum numbers.
Kind Regards, Mateusz Łącki
Files:
*********** input file taken by parameter2xml ********** MODEL_LIBRARY="/home/lacki/alpsdmrg/models.xml" LATTICE="open chain lattice" MODEL="SlonTrabalski" SWEEPS=8 NUMBER_EIGENVALUES=2
NUMSTATES=100
{L=10; V=0.1}
************* /home/lacki/alpsdmrg/models.xml ********** (I post only the modified things)
<BASIS name="spinc"> <SITEBASIS ref="spin"> <PARAMETER name="local_spin" value="local_S#"/> <PARAMETER name="local_S#" value="local_S"/> <PARAMETER name="local_S" value="1/2"/> </SITEBASIS> </BASIS>
<HAMILTONIAN name="SlonTrabalski"> <PARAMETER name="V" default="0"/> <BASIS ref="spinc"/> <SITETERM site="i"> V*Sx(i) </SITETERM> <BONDTERM source="i" target="j"> -(0.5)*(Splus(i)*Sminus(j)+Splus(j)*Sminus(i))-(0.5)*(Splus(i)*Splus(j)+Sminus(i)*Sminus(j)) </BONDTERM> </HAMILTONIAN>