Indeed periodic boundary conditions nee *many* more states and many more sweeps to converge well. What you observe is the reason why almost all DMRG simulations use open boundary conditions.
Matthias
On Mar 9, 2013, at 11:27 PM, Deepak Iyer deepak.g.iyer@gmail.com wrote:
As far as I know, DMRG works best with open boundaries. I'm not an expert though - but perhaps this is the source of the issue, the using periodic boundaries with DMRG needs some special code to deal with it correctly?
On Fri, Mar 8, 2013 at 10:19 AM, Emanuele Levi emanuele.levi@gmail.com wrote: Dear ALPS developers and users, I am running a DMRG simulation with alps on a Heisenberg chain with periodic boundary conditions. My parameter file is
'LATTICE' : "chain lattice", 'MODEL' : "spin", 'CONSERVED_QUANTUMNUMBERS' : 'Sz', 'L' : 24, 'Sz_total' : 0, 'Jxy' : 1, 'Jz' : 3, 'SWEEPS' : 4, 'NUM_WARMUP_STATES' : 100, 'MAXSTATES' : 100, 'NUMBER_EIGENVALUES' : 1, 'MEASURE_LOCAL[Local magnetization]' : 'Sz'In this regime I know the ground state has null global magnetization. As I am considering periodic boundaries, my results should be translationally invariant, and I should get a null local magnetization as well. Strangely enough though, when I check the local magnetization (last line of parameter file), I get a non-zero value. If I consider small L I find a local magnetization of the order E-7, which means practically 0. But when I grow the chain, this number rises, and in the case I am attaching is alternating, and of order 0.0275.
How could it be possible? Are not periodic boundary conditions enough to constrain to impose invariance under translation in the final state?
Moreover it really looks like considering more states and sweeping more doesn't help.
Thanks in advance for any help.
Kindest regards.
-- Emanuele Levi
emanuele.levi@gmail.com