Hi,
I would like to use the ALPS library (possibly mostly ED and DMRG) to study the Jaynes-Cummings-Hubbard model. Has anyone already implemented this model?
Below I include the most straightforward way I could think of and which produces the correct basis states but then I do not know how to use the <CONSTRAINT/> tag to pick out the subspace of constant total excitation number.
Alternatively I tried using the excitation number (i.e. boson plus spin) and spin quantum numbers as well as excitation number and boson number. In both cases I was not able to get the correct basis states (either I ended up with negative boson number or too large a spin projection).
Many thanks, Andreas
********************************************************* <MODELS>
<SITEBASIS name="JCHM">
<PARAMETER name="Nmax" default="infinity"/>
<QUANTUMNUMBER name="N" min="0" max="Nmax"/>
<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"/>
<OPERATOR name="bdag" matrixelement="sqrt(N+1)"> <CHANGE quantumnumber="N" change="1"/> </OPERATOR> <OPERATOR name="b" matrixelement="sqrt(N)"> <CHANGE quantumnumber="N" change="-1"/> </OPERATOR> <OPERATOR name="n" matrixelement="N"/>
<OPERATOR name="x" matrixelement="N+Sz+1/2"/>
</SITEBASIS>
<BASIS name="JCHM"> <SITEBASIS ref="JCHM"/> </BASIS>
<HAMILTONIAN name="JCHM"> <PARAMETER name="Delta" default="0"/> <PARAMETER name="g" default="1"/> <PARAMETER name="J" default="1"/> <BASIS ref="JCHM"/> <SITETERM site="i"> Delta*n(i) - g*(Sminus(i)*bdag(i) + Splus(i)*b(i)) </SITETERM> <BONDTERM source="i" target="j"> -J*(bdag(i)*b(j)+bdag(j)*b(i)) </BONDTERM> </HAMILTONIAN>
</MODELS>
*****************************************************************