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