Dear all,
I have been doing some tests for the Bose Hubbard model in 1D with dirloop_sse and I find that the the output density and the value of the Green's function at (0,0) do not coincide, as I would expect.
I understand that when measuring Green's functions for the Bose-Hubbard model the output is that of <b^\dagger_0 b_j> with j going over all lattice points. b^\dagger_i is a creation operator and b_j is a destruction at sites i and j respectively. If that is correct, then, the following should be correct too and I should get <b^\dagger_0 b_0>=<n_0>=\rho. Where I denote the density by \rho.
When I do the calculation, using the following input:
<?xml version="1.0" encoding="UTF-8"?> <?xml-stylesheet type="text/xsl" href="ALPS.xsl"?> <SIMULATION xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="http://xml.comp-phys.org/2003/8/QMCXML.xsd"> <PARAMETERS> <PARAMETER name="MEASURE[Green Function]">True</PARAMETER> <PARAMETER name="MEASURE[Correlations]">True</PARAMETER> <PARAMETER name="L">64</PARAMETER> <PARAMETER name="LATTICE">chain lattice</PARAMETER> <PARAMETER name="SEED">189185290</PARAMETER> <PARAMETER name="U">10.0</PARAMETER> <PARAMETER name="T">0.5</PARAMETER> <PARAMETER name="MODEL">boson Hubbard</PARAMETER> <PARAMETER name="Nmax">3</PARAMETER> <PARAMETER name="THERMALIZATION">1000</PARAMETER> <PARAMETER name="SWEEPS">50000</PARAMETER> <PARAMETER name="NONLOCAL">0</PARAMETER> <PARAMETER name="mu">0.4</PARAMETER> <PARAMETER name="t">0.5</PARAMETER> </PARAMETERS> </SIMULATION>
The output I get is:
<SCALAR_AVERAGE name="Density"> <COUNT>55257</COUNT> <MEAN method="simple">0.6790808</MEAN> <ERROR converged="yes" method="binning">0.000306</ERROR> <VARIANCE method="simple">0.00258</VARIANCE> <AUTOCORR method="binning">0.505</AUTOCORR>
<VECTOR_AVERAGE name="Green's Function" nvalues="64"> <SCALAR_AVERAGE indexvalue="( 0 ) -- ( 0 )"> <COUNT>55257</COUNT> <MEAN method="simple">1.178037</MEAN> <ERROR converged="yes" method="binning">0.000505</ERROR> <VARIANCE method="simple">0.0117</VARIANCE> <AUTOCORR method="binning">0.103</AUTOCORR>
Which is very different. Am I interpreting the output correctly or am I just not running it long enough?
Also, what is the meaning of the last three fields in the xml output field? n,n^2 and n^4? Because my initial guess would be to interpret n as the number of particles but it is not consistent with the density and the lattice size.
Thank you very much,
Francisco Cordobes
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