ALPS-users,

I am investigating the excitations of a Heisenberg exchange coupled  S=1 spin cluster as a function

of applied magnetic field and temperature.  All exchange constants are antiferromagnetic, and

the system can be thought of as a collection of a weakly coupled dimers.  I am starting with just

6 spins and will increase the elements later.  There are two exchanges and a single ion anisotropy

term (D) included in the Hamiltonian.  The GRAPH and HAMILTONIAN are pasted at the end

of this message.

For a given temperature and magnetic field, I would like to calculate the energy, S total quantum

number , and Sz total quantum number of the ground state and its excitations.

The total spin quantum number S, corresponds to the sum of the spin

vectors squared:

S^2 = (S_1 + S_2 + S_3 + …)^2, and

the Sz total quantum number corresponds to the sum of the S_nz values.

Sz = S_1z + S_2z + S_3z + …

Which algorithm do you suggest using for this problem?  Eventually, I would like to extend the

lattice to 12 spins and larger if possible.  Ultimately, I would like to know the ~10

lowest energy states and their S and Sz quantum numbers as a function of applied magnetic

field.

I am a beginner at ALPS, and have worked through some of the tutorials.  Any

suggestions would be very much appreciated.

Thanks,

Matthew Stone

----- dimerplanegraph.xml file-----

<LATTICES>

<!--

3 vertical dimers forming a triangle

-->

<GRAPH name="3dimers1plane" vertices="6">

    <VERTEX id="1"></VERTEX>

    <VERTEX id="2"></VERTEX>

    <VERTEX id="3"></VERTEX>

    <VERTEX id="4"></VERTEX>

    <VERTEX id="5"></VERTEX>

    <VERTEX id="6"></VERTEX>

    <EDGE type="0" source="1" target="2"/>

    <EDGE type="0" source="3" target="4"/>

    <EDGE type="0" source="5" target="6"/>

    <EDGE type="1" source="2" target="4"/>

    <EDGE type="1" source="2" target="6"/>

    <EDGE type="1" source="4" target="6"/>

    <EDGE type="1" source="1" target="3"/>

    <EDGE type="1" source="1" target="5"/>

    <EDGE type="1" source="3" target="5"/>

</GRAPH>

</LATTICES>

-----------------------------------------------

-----model-dspin.xml file-----

<MODELS>

<HAMILTONIAN name="BaMnO">

  <PARAMETER name="J0" default="J"/>

  <PARAMETER name="J1" default="J"/>

  <PARAMETER name="J" default="1"/>

  <PARAMETER name="h" default="0"/>

  <PARAMETER name="D" default="0"/>

  <BASIS ref="mixed spin"/>

  <SITETERM site="i">

    -h*Sz(i) + D*Sz(i)*Sz(i)

  </SITETERM>

  <BONDTERM type="0" source="i" target="j">

    J0*Sz(i)*Sz(j)+J0/2*(Splus(i)*Sminus(j)+Sminus(i)*Splus(j))

  </BONDTERM>

  <BONDTERM type="1" source="i" target="j">

    J1*Sz(i)*Sz(j)+J1/2*(Splus(i)*Sminus(j)+Sminus(i)*Splus(j))

  </BONDTERM>

</HAMILTONIAN>

<BASIS name="mixed spin">

  <SITEBASIS type="0" ref="spin">

    <PARAMETER name="local_spin" value="local_S"/>

    <PARAMETER name="local_S" value="1"/>

  </SITEBASIS>

  <SITEBASIS type="1" ref="spin">

    <PARAMETER name="local_spin" value="local_S'"/>

    <PARAMETER name="local_S'" value="1"/>

  </SITEBASIS>

  <CONSTRAINT quantumnumber="Sz" value="Sz_total"/>

</BASIS>

<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>

</MODELS>

--------------------------------------------------

Thank you,

Matthew B. Stone

Neutron Scattering Science Division

Oak Ridge National Laboratory

PO box 2008 MS6475

Oak Ridge, TN 37831-6475

Phone: 1-865-202-6898

Fax: 1-865-574-6080