SpinChainEntanglementEntropy

SpinChainEntanglementEntropy computes the entanglement spectrum and entanglement entropy of a spin chain. Its typical usage is

$PATHTODIAGHAM/build/Spin/src/Programs/SpinChainEntanglementEntropy spin_2_periodicaklt_p3_1.000000_p4_1.000000_n_8_sz_0_s_0_invsym_1_szsym_1_k_4.21.vec --use-lapack --use-svd

The --use-svd greatly improves the accuracy but only works when computing the entanglement spectrum of a single state. The code produces two output files whose name is deduced from the input vector, here spin_2_periodicaklt_p3_1.000000_p4_1.000000_n_8_sz_0_s_0_invsym_1_szsym_1_k_4.21.ent and spin_2_periodicaklt_p3_1.000000_p4_1.000000_n_8_sz_0_s_0_invsym_1_szsym_1_k_4.21.full.ent. The first one contains the entanglement entropies for all cuts up to the half the system size (unless the --min-la and/or --max-la options are used) and should look like

   1 1.6094379124341 1
   2 2.8249257205672 1
   3 3.7717695164438 1
   4 4.0513979917824 1

• The first column is number of sites in the region A.
• The second column is the Von Neumann entanglement entropy.
• The third column is the trace of the reduced matrix and should be equal to one.

The second file spin_2_periodicaklt_p3_1.000000_p4_1.000000_n_8_sz_0_s_0_invsym_1_szsym_1_k_4.21.full.ent stores the entanglement spectrum

   # l_a    Sz    lambda
   1 -4 0.2
   1 -2 0.2
   1 0 0.2
   1 2 0.2
   1 4 0.2
   2 -8 0.0060679611650486
   2 -6 0.027912621359223
   2 -6 0.0060679611650486
   2 -4 0.095873786407767
   ...

• The first column is number of sites in the region A.
• The second column is twice the <math>S_z</math> of the region A.
• The third column contains the eigenvalues of the reduced density matrix.