Dear Xingbo,
For a finite size MPS (matrix product state) the choice of periodic boundaries are really non-optimal. The problem, is that to represent entanglement between the beginning and the end of the chain one needs to propagate this information thought the whole length of the system. It usually means that one should work with ca. double the number of retained states M. Note that the complexity for the algorithm is M^3.
There could be other tricks to cancel boundary effects with some special fields at the boundaries or special boundary sites as has been done in the ALPS tutorials http://alps.comp-phys.org/mediawiki/index.php/ALPS_2_Tutorials:DMRG-01_DMRG#... http://alps.comp-phys.org/mediawiki/index.php/ALPS_2_Tutorials:DMRG-01_DMRG#Spin-1_Chain.
Additionally, note that the open boundary conditions could sometime lead to a simpler analysis of correlators, like the case of Friedel oscillations: Phys. Rev. B 65, 165122 and Phys. Rev. B 92, 195139.
Best regards, Michele
-- ETH Zurich Michele Dolfi Institute for Theoretical Physics HIT G 32.4 Wolfgang-Pauli-Str. 27 8093 Zurich Switzerland
dolfim@phys.ethz.ch www.itp.phys.ethz.ch
+41 44 633 78 56 phone +41 44 633 11 15 fax
On Apr 1, 2016, at 8:08 AM, 北尘心 740572900@qq.com wrote:
Dear all, I have a question about the boundary set.In the past, I use the boundary conditions is open boundary conditions in DMRG,but now i want to eliminate the impact of open boundary,so i need to use periodic boundary conditions.In the lattices file i find its setting ,like this:
<LATTICEGRAPH name = "inhomogeneous chain lattice"> <FINITELATTICE> <LATTICE ref="chain lattice"/> <EXTENT dimension="1" size ="L"/> <BOUNDARY type="periodic"/> </FINITELATTICE> <UNITCELL ref="simple1d"/> <INHOMOGENEOUS><VERTEX/></INHOMOGENEOUS> </LATTICEGRAPH>
but i still have a question about the accuracy of periodic boundary conditions,because i once read an paper on this question,it points out that DMRG offers much poorer results for problems with periodic boundary conditions (PBC) than for those with open boundary conditions(OBC),.The paper is attached. I wonder whether the problem has been solved. if yes,could you give me a paper with periodic boundary conditions to verify the correctness ?
In addition,if i want to set a smooth boundary condition,what should i do in the lattices file?
It is highly grateful for your any suggestions.
Yours sincerely,
Xingbo Wei Zhejiang Normal Universtiy, Jinhua, 230014, China <0404706.pdf>