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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