dirloop_sse density vs green's function measurement
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 .
Hi, which version of ALPS are you using? I'm checking with Sergei who wrote the code in 2.0, but the difference you see is basically 0.5, which is what you expect if the measurement is 0.5*( b^\dagger_0 b_j + b_j b^\dagger_0) Matthias On Jan 30, 2013, at 6:52 PM, Francisco Cordobés <ghiret@gmail.com> wrote:
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
.
Hi, I have tried both the current release and the r6722 release and happens with both. Francisco On 30 January 2013 17:59, Matthias Troyer <troyer@phys.ethz.ch> wrote:
Hi,
which version of ALPS are you using? I'm checking with Sergei who wrote the code in 2.0, but the difference you see is basically 0.5, which is what you expect if the measurement is 0.5*( b^\dagger_0 b_j + b_j b^\dagger_0)
Matthias
On Jan 30, 2013, at 6:52 PM, Francisco Cordobés <ghiret@gmail.com> wrote:
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
.
participants (2)
-
Francisco Cordobés
-
Matthias Troyer