Dear everyone, Does anyone know how to use the "coordinate " parameter in the models.xml file. I am trying to defining a quasi-periodic potential. But the "sparsediag" function does not recognize site "i". best regards!
Dear Cathy,
I’m not sure I fully get what if your goal. Here is anyway what I would do.
Usually for inhomogeneous models we define lattice sites with different type and set different values of the model parameters for each type.
Quick example: In mylattice.xml you define the graph <LATTICES> <GRAPH name="my great lattice" dimension="1" vertices=“3" edges="2"> <VERTEX id="1" type="0"><COORDINATE>0</COORDINATE></VERTEX> <VERTEX id="2" type="1"><COORDINATE>1</COORDINATE></VERTEX> <VERTEX id="3" type=“2"><COORDINATE>2</COORDINATE></VERTEX> <EDGE source="1" target="2" id="1" type="0" vector="1"/> <EDGE source="2" target="3" id="2" type="0" vector="1"/> </GRAPH> </LATTICES>
In the parameter file: LATTICE_LIBRARY="mylattice.xml" LATTICE="my great lattice" MODEL=“fermion Hubbard” t=1 U=8 mu0=0 mu1=10 mu2=5
This will have a different chemical potential for each of the three sites.
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 01 Jun 2015, at 18:31, Cathy Wu cathy.em2013@gmail.com wrote:
Dear everyone, Does anyone know how to use the "coordinate " parameter in the models.xml file. I am trying to defining a quasi-periodic potential. But the "sparsediag" function does not recognize site "i". best regards!
Dear Michele, it is very helpful and I FINALLY got some nice results. [?] good day!
2015-06-01 21:33 GMT+02:00 Michele Dolfi dolfim@phys.ethz.ch:
Dear Cathy,
I’m not sure I fully get what if your goal. Here is anyway what I would do.
Usually for inhomogeneous models we define lattice sites with different type and set different values of the model parameters for each type.
Quick example: In mylattice.xml you define the graph
<LATTICES> <GRAPH name="my great lattice" dimension="1" vertices=“3" edges="2"> <VERTEX id="1" type="0"><COORDINATE>0</COORDINATE></VERTEX> <VERTEX id="2" type="1"><COORDINATE>1</COORDINATE></VERTEX> <VERTEX id="3" type=“2"><COORDINATE>2</COORDINATE></VERTEX> <EDGE source="1" target="2" id="1" type="0" vector="1"/> <EDGE source="2" target="3" id="2" type="0" vector="1"/> </GRAPH> </LATTICES>
In the parameter file: LATTICE_LIBRARY="mylattice.xml" LATTICE="my great lattice" MODEL=“fermion Hubbard” t=1 U=8 mu0=0 mu1=10 mu2=5
This will have a different chemical potential for each of the three sites.
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 01 Jun 2015, at 18:31, Cathy Wu cathy.em2013@gmail.com wrote:
Dear everyone, Does anyone know how to use the "coordinate " parameter in the models.xml file. I am trying to defining a quasi-periodic potential. But the "sparsediag" function does not recognize site "i". best regards!
Dear Cathy,
The Michele's setting was sufficient for you, but there is another way of making inhomogeneous lattice. You can use "INHOMOGENEOUS" keyword in the lattice setting. In mylattice.xml, you can define the graph such as:
<LATTICES> <LATTICE name="chain lattice" dimension="1"> <PARAMETER name="a" default="1"/> <BASIS><VECTOR>a</VECTOR></BASIS> <RECIPROCALBASIS><VECTOR>2*pi/a</VECTOR></RECIPROCALBASIS> </LATTICE>
<UNITCELL name="simple1d" dimension="1"> <VERTEX/> <EDGE> <SOURCE vertex="1" offset="0"/> <TARGET vertex="1" offset="1"/> </EDGE> </UNITCELL>
<LATTICEGRAPH name = "inhomogeneous open chain lattice"> <FINITELATTICE> <LATTICE ref="chain lattice"/> <EXTENT dimension="1" size ="L"/> <BOUNDARY type="open"/> </FINITELATTICE> <UNITCELL ref="simple1d"/> <INHOMOGENEOUS><VERTEX/></INHOMOGENEOUS> </LATTICEGRAPH> </LATTICES>
"Inhomogeneous" tag is the most important tag here. If you set "LATTICEGRAPH" like this you can set the inhomogeneous site term as:
LATTICE_LIBRARY="mylattice.xml" LATTICE="inhomogeneous open chain lattice" MODEL="fermion Hubbard" L=15 t=1 U=-2 mu=-0.001*(x-L/2+0.5)^2
This setting corresponds to the fermions in the quadratic potential.
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