Dear all,
Since at least r7593 (end of July 2015), it is possible to study with MPS inhomogeneous systems, for example an 1D inhomogeneous Bose-Hubbard model with an harmonic trap by using 'inhomogeneous chain lattice' for the lattice and the following definition for the Hamiltonian
<HAMILTONIAN name="harm boson Hubbard"> <PARAMETER name="mu" default="0"/> <PARAMETER name="t" default="1"/> <PARAMETER name="V" default="0"/> <PARAMETER name="t'" default="0"/> <PARAMETER name="V'" default="0"/> <PARAMETER name="U" default="0"/> <PARAMETER name="t0" default="t"/> <PARAMETER name="t1" default="t'"/> <PARAMETER name="V0" default="V"/> <PARAMETER name="V1" default="V'"/> <PARAMETER name="K" default="0"/> <BASIS ref="boson"/> <SITETERM site="i"> <PARAMETER name="mu#" default="mu"/> <PARAMETER name="U#" default="U"/> <PARAMETER name="K#" default="K"/> -mu#*n(i)+U#*n(i)*(n(i)-1)/2+K#*n(i)*(x-0.5*(L-1))^2 </SITETERM> <BONDTERM source="i" target="j"> <PARAMETER name="t#" default="0"/> <PARAMETER name="V#" default="0"/> -t#*(bdag(i)*b(j)+bdag(j)*b(i)) + V#*n(i)*n(j) </BONDTERM> </HAMILTONIAN>
I would like to use an inhomogeneous BONDTERM. I tried things like -(t#+tharm#*(i+j-L)^2)*(bdag(i)*b(j)+bdag(j)*b(i)) or -(t#+tharm#*(x-0.5*(L-1))^2)*(bdag(i)*b(j)+bdag(j)*b(i)) in the definition of the Hamiltonian, but they all produce error messages indicating that mps_optim cannot evaluate such a Hamiltonian.
I thus have two questions: * Is inhomogeneous BONDTERM possible with MPS, and how to proceed? * MORE IMPORTANTLY: How can I figure out whether it is possible or not? I find nothing in the documentation, nothing in the Wiki. Is the only solution to look in the guts of the code, or to ask on the mailing list?
Thanks a lot in advance for your help.
Dominique
Dear Dominique,
Unfortunately inhomogeneous bond terms are not there (in the MPS codes).
For the moment you should fall back on having different bond types in your lattice definition.
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 Oct 6, 2015, at 12:50 PM, Dominique Delande Dominique.Delande@lkb.upmc.fr wrote:
Dear all,Since at least r7593 (end of July 2015), it is possible to study with MPS inhomogeneous systems, for example an 1D inhomogeneous Bose-Hubbard model with an harmonic trap by using 'inhomogeneous chain lattice' for the lattice and the following definition for the Hamiltonian
<HAMILTONIAN name="harm boson Hubbard"> <PARAMETER name="mu" default="0"/> <PARAMETER name="t" default="1"/> <PARAMETER name="V" default="0"/> <PARAMETER name="t'" default="0"/> <PARAMETER name="V'" default="0"/> <PARAMETER name="U" default="0"/> <PARAMETER name="t0" default="t"/> <PARAMETER name="t1" default="t'"/> <PARAMETER name="V0" default="V"/> <PARAMETER name="V1" default="V'"/> <PARAMETER name="K" default="0"/> <BASIS ref="boson"/> <SITETERM site="i"> <PARAMETER name="mu#" default="mu"/> <PARAMETER name="U#" default="U"/> <PARAMETER name="K#" default="K"/> -mu#*n(i)+U#*n(i)*(n(i)-1)/2+K#*n(i)*(x-0.5*(L-1))^2 </SITETERM> <BONDTERM source="i" target="j"> <PARAMETER name="t#" default="0"/> <PARAMETER name="V#" default="0"/> -t#*(bdag(i)*b(j)+bdag(j)*b(i)) + V#*n(i)*n(j) </BONDTERM> </HAMILTONIAN>
I would like to use an inhomogeneous BONDTERM. I tried things like -(t#+tharm#*(i+j-L)^2)*(bdag(i)*b(j)+bdag(j)*b(i)) or -(t#+tharm#*(x-0.5*(L-1))^2)*(bdag(i)*b(j)+bdag(j)*b(i)) in the definition of the Hamiltonian, but they all produce error messages indicating that mps_optim cannot evaluate such a Hamiltonian.
I thus have two questions:
- Is inhomogeneous BONDTERM possible with MPS, and how to proceed?
- MORE IMPORTANTLY: How can I figure out whether it is possible or not? I find nothing in the documentation, nothing in the Wiki. Is the only solution to look in the guts of the code, or to ask on the mailing list?
Thanks a lot in advance for your help.
Dominique
-- Dominique Delande (Dominique.Delande@lkb.upmc.fr) Laboratoire Kastler-Brossel - Case 74 - Universite P. et M. Curie 4, place Jussieu, F-75252 Paris Cedex 05, FRANCE Phone : +33 1 44 27 27 97 - Fax : +33 1 44 27 38 45 Acces : Tour 13, Couloir 12-13, 3eme etage - Bureau 316
Dear Dominique,
Since version r7645 you can now specify inhomogeneous bonds in the MPS codes.
Be aware that x/y/z for bonds correspond the coordinate of the middle point on the bond. To define inhomogeneous sites and bonds you have to create a custom lattice with <INHOMOGENEOUS><VERTEX/><EDGE/></INHOMOGENEOUS>.
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 Oct 6, 2015, at 1:50 PM, Michele Dolfi dolfim@phys.ethz.ch wrote:
Dear Dominique,
Unfortunately inhomogeneous bond terms are not there (in the MPS codes).
For the moment you should fall back on having different bond types in your lattice definition.
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 mailto:dolfim@phys.ethz.ch www.itp.phys.ethz.ch http://www.itp.phys.ethz.ch/
+41 44 633 78 56 phone +41 44 633 11 15 fax
On Oct 6, 2015, at 12:50 PM, Dominique Delande <Dominique.Delande@lkb.upmc.fr mailto:Dominique.Delande@lkb.upmc.fr> wrote:
Dear all,Since at least r7593 (end of July 2015), it is possible to study with MPS inhomogeneous systems, for example an 1D inhomogeneous Bose-Hubbard model with an harmonic trap by using 'inhomogeneous chain lattice' for the lattice and the following definition for the Hamiltonian
<HAMILTONIAN name="harm boson Hubbard"> <PARAMETER name="mu" default="0"/> <PARAMETER name="t" default="1"/> <PARAMETER name="V" default="0"/> <PARAMETER name="t'" default="0"/> <PARAMETER name="V'" default="0"/> <PARAMETER name="U" default="0"/> <PARAMETER name="t0" default="t"/> <PARAMETER name="t1" default="t'"/> <PARAMETER name="V0" default="V"/> <PARAMETER name="V1" default="V'"/> <PARAMETER name="K" default="0"/> <BASIS ref="boson"/> <SITETERM site="i"> <PARAMETER name="mu#" default="mu"/> <PARAMETER name="U#" default="U"/> <PARAMETER name="K#" default="K"/> -mu#*n(i)+U#*n(i)*(n(i)-1)/2+K#*n(i)*(x-0.5*(L-1))^2 </SITETERM> <BONDTERM source="i" target="j"> <PARAMETER name="t#" default="0"/> <PARAMETER name="V#" default="0"/> -t#*(bdag(i)*b(j)+bdag(j)*b(i)) + V#*n(i)*n(j) </BONDTERM> </HAMILTONIAN>
I would like to use an inhomogeneous BONDTERM. I tried things like -(t#+tharm#*(i+j-L)^2)*(bdag(i)*b(j)+bdag(j)*b(i)) or -(t#+tharm#*(x-0.5*(L-1))^2)*(bdag(i)*b(j)+bdag(j)*b(i)) in the definition of the Hamiltonian, but they all produce error messages indicating that mps_optim cannot evaluate such a Hamiltonian.
I thus have two questions:
- Is inhomogeneous BONDTERM possible with MPS, and how to proceed?
- MORE IMPORTANTLY: How can I figure out whether it is possible or not? I find nothing in the documentation, nothing in the Wiki. Is the only solution to look in the guts of the code, or to ask on the mailing list?
Thanks a lot in advance for your help.
Dominique
-- Dominique Delande (Dominique.Delande@lkb.upmc.fr mailto:Dominique.Delande@lkb.upmc.fr) Laboratoire Kastler-Brossel - Case 74 - Universite P. et M. Curie 4, place Jussieu, F-75252 Paris Cedex 05, FRANCE Phone : +33 1 44 27 27 97 - Fax : +33 1 44 27 38 45 Acces : Tour 13, Couloir 12-13, 3eme etage - Bureau 316
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