On a finite size system there is no spontaneous symmetry breaking and you will thus not see Neel order by looking at local magnetizations. It can only be detected looking at correlation functions

Matthias



On 23 Jun 2010, at 18:20, Jun Wen wrote:

I am not sure. I am considering the AF Heisenberg where a Neel order should arise as the ground state and I expect staggered magnetization on square lattice. Therefore, the local spin for each site would be different. 



On Wed, Jun 23, 2010 at 11:15 PM, Matthias Troyer <troyer@phys.ethz.ch> wrote:
Can't you just divide by the number of sites if it measures the total spin?

On 23 Jun 2010, at 18:10, Jun Wen wrote:

you are right! However, the problem is that I want to measure the local spin for each site, and it seems to me that if I use the following 

MEASURE_AVERAGE[Sz]=Sz;

it will measure the total Sz, not the Sz at each site. 

Am I wrong about it?

Best,
Jun


On Wed, Jun 23, 2010 at 10:36 PM, Matthias Troyer <troyer@phys.ethz.ch> wrote:
It is better to use MEASURE_AVERAGE instead of MEASURE_LOCAL. That way you keep the translation symmetry and the reduction it brings in Hilbert space dimension.

Matthias

On 23 Jun 2010, at 16:43, jun wen wrote:

> Hello Matthias,
>
> Thanks for your message. You are right! I found that once I use the
> graph(where translation symmetry is absent)  instead of lattice graph
> (where translation symmetry is present) to construct the lattice, then
> the local quantities can be computed via ED.
>
>
> Best regards,
> Jun
>
>
>
> On Wed, Jun 23, 2010 at 6:55 PM, Matthias Troyer <troyer@phys.ethz.ch> wrote:
>> The reason is probably that your lattice is translation invariant - then only average quantities and not local ones are computed, since all local quantities would be the same.
>>
>> Matthias
>>
>>
>> On 21 Jun 2010, at 08:33, jun wen wrote:
>>
>>> Hello All,
>>>
>>> I was trying to compute the local <S> in the Kitaev model defined on
>>> the honeycomb lattice with Exact Diagnolization
>>> Here is my parameter file:
>>>
>>> MODEL="kitaev";
>>> LATTICE="honeycomb lattice";
>>>
>>> LATTICE_LIBRARY="../../../definitions/kitaev/lattices.xml";
>>> MODEL_LIBRARY="../../../definitions/kitaev/models.xml";
>>>
>>> MEASURE_LOCAL[Local Sz]=Sz;
>>> MEASURE_LOCAL[Local Sx]=Sx;
>>> MEASURE_LOCAL[Local Sy]=Sy;
>>>
>>> local_S=1/2;
>>> L=2;
>>> W=2;
>>> J=1;
>>>
>>> However, in the output xml file, there are no such terms as the Local
>>> Sz or Local Splux or Local Sminus.
>>> I wonder if anyone could kindly point out what is the problem.  The
>>> Kitaev model is defined in the following models.xml
>>> Thanks a lot!
>>>
>>> <MODELS>
>>> <SITEBASIS name="spin">
>>>  <PARAMETER name="local_spin" default="local_S"/>
>>>  <PARAMETER name="local_S" default="1/2"/>
>>>  <QUANTUMNUMBER name="S" min="local_spin" max="local_spin"/>
>>>  <QUANTUMNUMBER name="Sz" min="-S" max="S"/>
>>>  <OPERATOR name="Splus" matrixelement="sqrt(S*(S+1)-Sz*(Sz+1))">
>>>    <CHANGE quantumnumber="Sz" change="1"/>
>>>  </OPERATOR>
>>>  <OPERATOR name="Sminus" matrixelement="sqrt(S*(S+1)-Sz*(Sz-1))">
>>>    <CHANGE quantumnumber="Sz" change="-1"/>
>>>  </OPERATOR>
>>>  <OPERATOR name="Sz" matrixelement="Sz"/>
>>> </SITEBASIS>
>>>
>>>
>>> <SITEOPERATOR name="Sx" site="x">
>>>  1/2*(Splus(x)+Sminus(x))
>>> </SITEOPERATOR>
>>>
>>> <SITEOPERATOR name="Sy" site="x">
>>>  1/2/I*(Splus(x)-Sminus(x))
>>> </SITEOPERATOR>
>>>
>>> <BASIS name="spin">
>>>  <SITEBASIS ref="spin"/>
>>> </BASIS>
>>>
>>> <HAMILTONIAN name="kitaev">
>>>
>>>  <PARAMETER name="J1" default="1"/>
>>>  <PARAMETER name="Jz" default="J1"/>
>>>  <PARAMETER name="Jx" default="J1"/>
>>>  <PARAMETER name="Jy" default="J1"/>
>>>
>>>  <BASIS ref="spin"/>
>>>
>>>  <BONDTERM type="0" source="i" target="j">
>>>    Jz*Sz(i)*Sz(j)
>>>  </BONDTERM>
>>>
>>> <BONDTERM type="1" source="i" target="j">
>>>    Jx*Sx(i)*Sx(j)
>>>
>>>  </BONDTERM>
>>>
>>> <BONDTERM type="2" source="i" target="j">
>>>    Jy*Sy(i)*Sy(j)
>>>
>>>  </BONDTERM>
>>> </HAMILTONIAN>
>>>
>>> </MODELS>
>>>
>>> Jun
>>>
>>
>>
>




--
Jun Wen, Graduate Research Assistant
Office: RLM 7.312
Department of Physics
1 University Station C1600
The University of Texas at Austin
TX, 78712
Email:  jwen@physics.utexas.edu
          junwen.ut@gmail.com




--
Jun Wen, Graduate Research Assistant
Office: RLM 7.312
Department of Physics
1 University Station C1600
The University of Texas at Austin
TX, 78712
Email:  jwen@physics.utexas.edu
          junwen.ut@gmail.com