This is something that I personally never tried, but here is maybe a starting point to develop further.
Define a graph (unfortunately there will be no generic lattice for this) like: * a photons reservoir: <VERTEX type=1 id=1 /> * the usual sites: <VERTEX type=0 id=2 /> <VERTEX type=0 id=3 /> <VERTEX type=0 id=4 /> … * edges between usual sites, e.g. a chain: <EDGE source=“2" target=“3" id="1" type="0" vector="1"/> <EDGE source=“3" target=“4" id="2" type="0" vector="1"/> <EDGE source=“4" target=“5" id="3" type="0" vector="1"/> … * edge between atoms and photon reservoir: <EDGE source=“1" target=“2" id=“4" type=“1"/> <EDGE source=“1" target=“3" id=“5" type=“1"/> <EDGE source=“1" target=“4" id=“6" type=“1"/>
Then for the model.
<BASIS name=“photon lattice"> <SITEBASIS type="0" ref="fermion"/> <SITEBASIS type="1" ref=“bosons”/> <— this will be your photons </BASIS>
In the Hamiltonian you can then define terms like: t0*cdag_up(i)*c_up(j) <— for the usual particles t1*bdag(i)*c_up(j) <— for photon-atom interactions
Note that on the single site hosting all photons you need to define a cutoff, e.g. Nmax=100. (for some codes this cutoff can make the calculation very expensive!)
Best regards, Michele
-- ETH Zurich Michele Dolfi Institute for Theoretical Physics HIT G 32.4 Wolfgang-Pauli-Str. 27 8093 Zurich Switzerland
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On 05 May 2016, at 11:13, 梁霄 lxxhlb@mail.ustc.edu.cn wrote:
Dear all, In alps models all the basis are defined on site positions. When there are interactions between atoms and photons, an atom on each site can absorb or emit photons, how to define such basis for photons? Thanks.
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