PeriodicSpinChainGeneralizedAKLT

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PeriodicSpinChainGeneralizedAKLT performs the exact diagonalization of the spin 2 analogue of the AKLT Hamiltonian. We denote <math>P^{(s)}_{i,j}</math> the projector on the total spin <math>s</math> sector for the two spins located on sites <math>i</math> and <math>j</math>. The generalized AKLT hamiltonian for a chain of $N$ spins with periodic boundary conditions reads

<math>H=\sum_{i=0}^{N-1} \lambda^{(3)} P^{(3)}_{i,i+1} + \lambda^{(4)} P^{(4)}_{i,i+1} </math>

PeriodicSpinChainGeneralizedAKLT supports the same features than PeriodicSpinChainAKLT, including all discrete symmetries, real hamiltonians / vectors when available, ... The two coefficients <math>\lambda^{(3)}</math> and <math>\lambda^{(4)}</math> are set by the options --p3-factor and --p4-factor . Their values appear in the output file names. For example

$PATHTODIAGHAM/build/Spin/src/Programs/PeriodicSpinChainGeneralizedAKLT -p 2 --p3-factor 1.0 --p4-factor 1.0 --use-lapack

will generate a file spin_2_periodicaklt_p3_1.000000_p4_1.000000_n_2.dat containing the spectrum for these parameters. The file content should look like

   #  periodic spin 2 chain with 2 sites 
   # 2Sz K SzSym InvSym  E
   0 0 1 1  0
   0 0 1 1  2.0816681711722e-17
   0 0 1 1  2
   0 1 -1 1  0
   0 1 -1 1  2
   2 0 0 1 1.1102230246252e-16
   2 0 0 1 2
   2 1 0 1 -1.6653345369377e-16
   2 1 0 1 2
   4 0 0 1 -1.1102230246252e-16
   4 0 0 1 2
   4 1 0 1 2
   6 0 0 1 2
   6 1 0 1 2
   8 0 0 1 2