Dear All,
I'm using ALPS DMRG (MPS) to study the magnetism of XY model in a frustrated chain.
In order to obtain the Sx correlation functions, I add the following command line: MEASURE_CORRELATIONS[Sx_correlation]= Sx
I expected that the output file presented me all <Sx(i) Sx(j)> correlation functions. However, there were only this line in the output file.
<SCALAR_AVERAGE name="Sx_correlation"><MEAN>6.7066684180584175e-317</MEAN></SCALAR_AVERAGE>
Even when I chose to program make only specifics calculations, such as
MEASURE_LOCAL_AT[SxSx_corr] = "Sx:Sx|(0,1),(0,2),(0,3),(0,4)"
the answer I obtained was zero, no matter of the choice of the external parameters, as showed below.
<VECTOR_AVERAGE name="SxSx_corr"> <SCALAR_AVERAGE indexvalue="( 0 ) -- ( 0 )"><MEAN>0</MEAN></SCALAR_AVERAGE> <SCALAR_AVERAGE indexvalue="( 0 ) -- ( 0 )"><MEAN>0</MEAN></SCALAR_AVERAGE> <SCALAR_AVERAGE indexvalue="( 0 ) -- ( 1 )"><MEAN>0</MEAN></SCALAR_AVERAGE> <SCALAR_AVERAGE indexvalue="( 0 ) -- ( 1 )"><MEAN>0</MEAN></SCALAR_AVERAGE> </VECTOR_AVERAGE>
*(the index are not the same in the input and output file because I'm working with a unit cell with 3 sites.)
Owing to these not good results, I did a test, and then I measured the correlation functions <Splus(i) Splus(j)>, <Splus(i) Sminus(j)> and <Sminus(i) Sminus(j)>, as showed below
MEASURE_LOCAL_AT[SxSx_corr1] = "Splus:Splus|(3,18)" MEASURE_LOCAL_AT[SxSx_corr2] = "Splus:Sminus|(3,18)" MEASURE_LOCAL_AT[SxSx_corr3] = "Sminus:Splus|(3,18)" MEASURE_LOCAL_AT[SxSx_corr4] = "Sminus:Sminus|(3,18)"
and I obtained
<VECTOR_AVERAGE name="SxSx_corr1"> <SCALAR_AVERAGE indexvalue="( 1 ) -- ( 6 )"><MEAN>-0.1565028679350004</MEAN></SCALAR_AVERAGE>
</VECTOR_AVERAGE> <VECTOR_AVERAGE name="SxSx_corr2"> <SCALAR_AVERAGE indexvalue="( 1 ) -- ( 6 )"><MEAN>-0.15912792472820933</MEAN></SCALAR_AVERAGE>
</VECTOR_AVERAGE>
<VECTOR_AVERAGE name="SxSx_corr3"> <SCALAR_AVERAGE indexvalue="( 1 ) -- ( 6 )"><MEAN>-0.15912792472820814</MEAN></SCALAR_AVERAGE> </VECTOR_AVERAGE>
<VECTOR_AVERAGE name="SxSx_corr4"> <SCALAR_AVERAGE indexvalue="( 1 ) -- ( 6 )"><MEAN>-0.15650286793499901</MEAN></SCALAR_AVERAGE> </VECTOR_AVERAGE>
which means that <SxSx>'s are really nonzero. Actually, these last results are in good agreement with exact diagonalization for a small chain. (Before you asked me, I correctly defined the onsite operator Sx in the model library.)
Then, probably it could be a bug when the program is summing the terms of SxSx correlations.
I really thank you for this great program.
Regards,
Natanael C. Costa