Dear Matthias:

  I begin with the Hamiltonian for a chain with spins S=1/2 ,

    

   use periodic boundary conditions ,the total number of sites is N=20. calculate correlation :

  Offdiagonal spin correlations  has problem,

    why 0-0  and  0-1   offdiagonal spin  correlations  value is 0   ??

[( 0 ) -- ( 0 )]	0
Offdiagonal spin correlations[( 0 ) -- ( 1 )]	0
Offdiagonal spin correlations[( 1 ) -- ( 0 )]	0.2499999999999999
Offdiagonal spin correlations[( 1 ) -- ( 1 )]	0.01195256946918583
Offdiagonal spin correlations[( 0 ) -- ( 1 )]	-0.1410917216909388
Offdiagonal spin correlations[( 0 ) -- ( 2 )]	-0.02578705926914329
Offdiagonal spin correlations[( 1 ) -- ( 1 )]	0.05437436640436828
Offdiagonal spin correlations[( 1 ) -- ( 2 )]	0.01374443422199295
Offdiagonal spin correlations[( 0 ) -- ( 2 )]	-0.04722700778251831
Offdiagonal spin correlations[( 0 ) -- ( 3 )]	-0.01673969792911871
Offdiagonal spin correlations[( 1 ) -- ( 2 )]	0.06699300813943075
Offdiagonal spin correlations[( 1 ) -- ( 3 )]	0.002194337470049455
Offdiagonal spin correlations[( 0 ) -- ( 3 )]	-0.03664352593820266
Offdiagonal spin correlations[( 0 ) -- ( 4 )]	0.002203905249778245
Offdiagonal spin correlations[( 1 ) -- ( 3 )]	0.0331275686776057
Offdiagonal spin correlations[( 1 ) -- ( 4 )]	-0.007827950318578362
Offdiagonal spin correlations[( 0 ) -- ( 4 )]	-0.04668994676799755
Offdiagonal spin correlations[( 0 ) -- ( 5 )]	0.01338526650557481
Offdiagonal spin correlations[( 1 ) -- ( 4 )]	0.05418339350735944
Offdiagonal spin correlations[( 1 ) -- ( 5 )]	-0.02572536103232437
Offdiagonal spin correlations[( 0 ) -- ( 5 )]	0
Offdiagonal spin correlations[( 0 ) -- ( 6 )]	0
Offdiagonal spin correlations[( 1 ) -- ( 5 )]	0.01195256946918583
Offdiagonal spin correlations[( 1 ) -- ( 6 )]	0.2499999999999999
Offdiagonal spin correlations[( 0 ) -- ( 6 )]	0.01194311395908962
Offdiagonal spin correlations[( 0 ) -- ( 7 )]	-0.1411693721423247
Offdiagonal spin correlations[( 1 ) -- ( 6 )]	-0.02576129524991342
Offdiagonal spin correlations[( 1 ) -- ( 7 )]	0.05444259724942019
Offdiagonal spin correlations[( 0 ) -- ( 7 )]	0.01371611664136257
Offdiagonal spin correlations[( 0 ) -- ( 8 )]	-0.09445304446831181
Offdiagonal spin correlations[( 1 ) -- ( 7 )]	-0.01667478948175052
Offdiagonal spin correlations[( 1 ) -- ( 8 )]	0.03335169908714469
Offdiagonal spin correlations[( 0 ) -- ( 8 )]	0.002207364935941955
Offdiagonal spin correlations[( 0 ) -- ( 9 )]	-0.03640998935519778
Offdiagonal spin correlations[( 1 ) -- ( 8 )]	0.00226127678640559
Offdiagonal spin correlations[( 1 ) -- ( 9 )]	0.03307792417161022
Offdiagonal spin correlations[( 0 ) -- ( 9 )]	-0.008440335344440209
Offdiagonal spin correlations[( 0 ) -- ( 10 )]	-0.04669087903965578
Offdiagonal spin correlations[( 1 ) -- ( 9 )]	0.01383912437540501
Offdiagonal spin correlations[( 1 ) -- ( 10 )]	0.05428792435810501