[ALPS-users] 答复: 答复: How to count dimension of graph defined in Lattice xml library

Sun Rongyang sun-rongyang at outlook.com
Fri Nov 10 02:30:13 CET 2017 

Dear Troyer,

Thanks so much for your patience. I will show more details about my puzzle. First, I design a pure GRAPH:

*******************************************************************************
<GRAPH name="anisotropic open ladder graph test">
    <!-- type="0" means horizontal; type="1" means vertical -->
    <EDGE tyep="0" source="1" target="2"/>
    <EDGE tyep="0" source="2" target="3"/>
    <EDGE tyep="0" source="3" target="4"/>
    <EDGE tyep="0" source="4" target="5"/>
    <EDGE tyep="0" source="6" target="7"/>
    <EDGE tyep="0" source="7" target="8"/>
    <EDGE tyep="0" source="8" target="9"/>
    <EDGE tyep="0" source="9" target="10"/>
    <EDGE tyep="1" source="1" target="6"/>
    <EDGE tyep="1" source="2" target="7"/>
    <EDGE tyep="1" source="3" target="8"/>
    <EDGE tyep="1" source="4" target="9"/>
    <EDGE tyep="1" source="5" target="10"/>
</GRAPH>
*******************************************************************************
Then I design a MODEL:

*******************************************************************************
<HAMILTONIAN name="anisotropic Heisenberg">
    <!-- Jh: J horizontal -->
    <!-- Jv: J vertical -->
    <PARAMETER name="Jh" default="0"/>
    <PARAMETER name="Jv" default="0"/>
    <BASIS ref="spin"/>
    <BONDTERM type="0" source="i" target="j">
    <!--  type="0" means horizontal -->
        Jh*exchange(i,j)
    </BONDTERM>
    <BONDTERM type="1" source="i" target="j">
    <!-- type="1" means vertical -->
        Jv*exchange(i,j)
    </BONDTERM>
</HAMILTONIAN>
*******************************************************************************
Then I run mps_evolve from a local_quantumnumbers:

*************************************
up   down up   down up
+----+----+----+----+
|    |    |    |    |
|    |    |    |    |
+----+----+----+----+
down up   down up   down
**************************************
with Jh=0.1 and Jv=1.0.
The Energy of the system is -0.325. I guess -0.325 means 1/4 * 0.1 * 13 all the edges have been seen as type="0" edge. The right answer should be -1.45. I do not know what happened here.

Best regards,
Rongyang Sun




________________________________
发件人: Comp-phys-alps-users <comp-phys-alps-users-bounces at lists.phys.ethz.ch> 代表 Matthias Troyer <troyer at phys.ethz.ch>
发送时间: 2017年11月9日 17:54
收件人: comp-phys-alps-users at lists.phys.ethz.ch
主题: Re: [ALPS-users] 答复: How to count dimension of graph defined in Lattice xml library

Yes that should work.

On 10 Nov 2017, at 00:00, Sun Rongyang <sun-rongyang at outlook.com<mailto:sun-rongyang at outlook.com>> wrote:

Dear Troyer,

Thanks so much for your response. Your answer has solved my question. I am sorry but I have another small question here. Whether a pure graph can use "type" attribute in EDGE as in a UNITCELL? I tried to use it but got some puzzling results.

Best regards,
Rongyang


________________________________
发件人: Comp-phys-alps-users <comp-phys-alps-users-bounces at lists.phys.ethz.ch<mailto:comp-phys-alps-users-bounces at lists.phys.ethz.ch>> 代表 Matthias Troyer <troyer at phys.ethz.ch<mailto:troyer at phys.ethz.ch>>
发送时间: 2017年11月9日 7:19
收件人: comp-phys-alps-users at lists.phys.ethz.ch<mailto:comp-phys-alps-users at lists.phys.ethz.ch>
主题: Re: [ALPS-users] How to count dimension of graph defined in Lattice xml library

Arbitrary graphs don’t have a “dimension”. Only lattices do.

On 9 Nov 2017, at 14:12, Sun Rongyang <sun-rongyang at outlook.com<mailto:sun-rongyang at outlook.com>> wrote:

Dear all,

The definition method of a lattice in ALPS is delicate. But I meet a problem about dimension counting of a pure graph. On the one hand, I define an pure anisotropic graph as:

*************************************************************************************************
<GRAPH name="anisotropic open ladder graph test">
    <!-- type="0" means horizontal; type="1" means vertical -->
    <EDGE tyep="0" source="1" target="2"/>
    <EDGE tyep="0" source="2" target="3"/>
    <EDGE tyep="0" source="3" target="4"/>
    <EDGE tyep="0" source="4" target="5"/>
    <EDGE tyep="0" source="6" target="7"/>
    <EDGE tyep="0" source="7" target="8"/>
    <EDGE tyep="0" source="8" target="9"/>
    <EDGE tyep="0" source="9" target="10"/>
    <EDGE tyep="1" source="1" target="6"/>
    <EDGE tyep="1" source="2" target="7"/>
    <EDGE tyep="1" source="3" target="8"/>
    <EDGE tyep="1" source="4" target="9"/>
    <EDGE tyep="1" source="5" target="10"/>
</GRAPH>
*************************************************************************************************
On the other hand, I use the default LATTICEGRAPH "open ladder", I copy here:

*************************************************************************************************
<LATTICE name="square lattice" dimension="2">
  <PARAMETER name="a" default="1"/>
  <BASIS><VECTOR>a 0</VECTOR><VECTOR>0 a</VECTOR></BASIS>
  <RECIPROCALBASIS><VECTOR>2*pi/a 0</VECTOR><VECTOR>0 2*pi/a</VECTOR></RECIPROCALBASIS>
</LATTICE>

<UNITCELL name="anisotropic2d" dimension="2">
  <VERTEX/>
  <EDGE type="0"><SOURCE vertex="1" offset="0 0"/><TARGET vertex="1" offset="1 0"/></EDGE>
  <EDGE type="1"><SOURCE vertex="1" offset="0 0"/><TARGET vertex="1" offset="0 1"/></EDGE>
</UNITCELL>

<LATTICEGRAPH name = "open ladder" vt_name="OpenLadderLattice">
  <FINITELATTICE>
    <LATTICE ref="square lattice"/>
    <PARAMETER name="W" default="2"/>
    <EXTENT dimension="1" size="L"/>
    <EXTENT dimension="2" size="W"/>
    <BOUNDARY dimension="1" type="open"/>
    <BOUNDARY dimension="2" type="open"/>
  </FINITELATTICE>
  <UNITCELL ref="anisotropic2d"/>
</LATTICEGRAPH>
*************************************************************************************************
with parameters L=2, W=5. Will they be treated as the same in ALPS? Or the graph equals as L=5,W=2 open ladder?

Thanks a lot!

Best regards,
Rongyang Sun





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