Reduced Density Matrices¶
- ctm.one_site_c4v_abelian.rdm_c4v.rdm1x1(state, env, sym_pos_def=False, force_cpu=False, verbosity=0, **kwargs)[source]¶
- Parameters:
state (IPEPS_ABELIAN_C4V) – underlying wavefunction
env (ENV_ABELIAN_C4V) – environment corresponding to
state
verbosity (int) – logging verbosity
force_cpu (bool) – perform on CPU
- Returns:
1-site reduced density matrix with indices \(s;s'\)
- Return type:
yastn.Tensor
Computes 1-site reduced density matrix \(\rho_{1x1}\) centered on vertex
coord
by contracting the following tensor network:----> C--T-----C A | | | | | T--a^+a--T | | | | | V C--T-----C <----
where the physical indices s and s’ of on-site tensor \(A\) at vertex
coord
and it’s hermitian conjugate \(A^\dagger\) are left uncontracted
- ctm.one_site_c4v_abelian.rdm_c4v.rdm2x1(state, env, sym_pos_def=False, force_cpu=False, verbosity=0, **kwargs)[source]¶
- Parameters:
state (IPEPS_ABELIAN_C4V) – underlying 1-site C4v symmetric wavefunction
env (ENV_ABELIAN_C4V) – C4v symmetric environment corresponding to
state
sym_pos_def (bool) – make final density matrix symmetric and non-negative (default: False)
force_cpu (bool) – perform on CPU
verbosity (int) – logging verbosity
- Returns:
2-site reduced density matrix with indices \(s_0s_1;s'_0s'_1\)
- Return type:
yastn.Tensor
Computes 2-site reduced density matrix \(\rho_{2x1}\) of a horizontal 2x1 subsystem using following strategy:
compute upper left 2x2 corner and lower left 2x1 corner
construct left half of the network
contract left and right half (identical to the left) to obtain final reduced density matrix
----> C--T-----T-----C = C2x2--C2x2 | | | | | | T--a^+a--a^+a--T C2x1--C2x1 | | | | C--T-----T-----C <----
The physical indices s and s’ of on-sites tensors \(a\) (and \(a^\dagger\)) are left uncontracted and given in the following order:
s0 s1
The resulting reduced density matrix is identical to the one of vertical 1x2 subsystem due to the C4v symmetry.
- ctm.one_site_c4v_abelian.rdm_c4v.rdm2x2_NN(state, env, sym_pos_def=False, force_cpu=False, verbosity=0, **kwargs)[source]¶
- Parameters:
state (IPEPS_ABELIAN_C4V) – underlying 1-site C4v symmetric wavefunction
env (ENV_ABELIAN_C4V) – C4v symmetric environment corresponding to
state
sym_pos_def (bool) – make final density matrix symmetric and non-negative (default: False)
force_cpu (bool) – compute on cpu
verbosity (int) – logging verbosity
- Returns:
2-site reduced density matrix with indices \(s_0s_1;s'_0s'_1\)
- Return type:
yastn.Tensor
Computes 2-site reduced density matrix \(\rho_{2x1}\) of 2 sites that are nearest neighbours using strategy:
compute upper left corner using double-layer on-site tensor
construct upper half of the network
contract upper and lower half (identical to upper) to obtain final reduced density matrix
C--T-----T-----C = C2x2c--C2x2--s0,s'0 A | | | | | | | | T--a^+a--a^+a--T | C2x2c--C2x2--s1,s'1 | | | | | V T--a^+a--a^+a--T | | | | C--T-----T-----C
The physical indices s and s’ of on-sites tensors \(a\) (and \(a^\dagger\)) inside C2x2 tensors are left uncontracted and given in the following order:
c s0,s'0 c s1,s'1
- ctm.one_site_c4v_abelian.rdm_c4v.rdm2x2_NNN(state, env, sym_pos_def=False, force_cpu=False, verbosity=0, **kwargs)[source]¶
- Parameters:
state (IPEPS_ABELIAN_C4V) – underlying 1-site C4v symmetric wavefunction
env (ENV_ABELIAN_C4V) – C4v symmetric environment corresponding to
state
sym_pos_def (bool) – make final density matrix symmetric and non-negative (default: False)
force_cpu (bool) – compute on cpu
verbosity (int) – logging verbosity
- Returns:
2-site reduced density matrix with indices \(s_0s_1;s'_0s'_1\)
- Return type:
yastn.Tensor
Computes 2-site reduced density matrix \(\rho_{2x1}^{diag}\) of 2 sites that are next-nearest neighbours (along diagonal) using strategy:
compute upper left corner using double-layer on-site tensor
construct upper half of the network
contract upper and lower half (identical to upper) to obtain final reduced density matrix
C--T-----T-----C = C2x2c--C2x2 A | | | | | | | | T--a^+a--a^+a--T | C2x2---C2x2c | | | | | V T--a^+a--a^+a--T | | | | C--T-----T-----C
The physical indices s and s’ of on-sites tensors \(A\) (and \(A^\dagger\)) inside C2x2 tensors are left uncontracted and given in the following order:
c s0 s1 c
- ctm.one_site_c4v_abelian.rdm_c4v.rdm2x2(state, env, sym_pos_def=False, force_cpu=False, verbosity=0, **kwargs)[source]¶
- Parameters:
state (IPEPS_ABELIAN_C4V) – underlying 1-site C4v symmetric wavefunction
env (ENV_ABELIAN_C4V) – C4v symmetric environment corresponding to
state
sym_pos_def (bool) – make final density matrix symmetric and non-negative (default: False)
force_cpu (bool) – perform on CPU
verbosity (int) – logging verbosity
- Returns:
4-site reduced density matrix with indices \(s_0s_1s_2s_3;s'_0s'_1s'_2s'_3\)
- Return type:
yastn.Tensor
Computes 4-site reduced density matrix \(\rho_{2x2}\) of 2x2 subsystem using strategy:
compute upper left corner
construct upper half of the network
contract upper and lower half (identical to upper) to obtain final reduced density matrix
C--T-----T-----C = C2x2--C2x2 A | | | | | | | | T--a^+a--a^+a--T | C2x2--C2x2 | | | | | V T--a^+a--a^+a--T | | | | C--T-----T-----C
The physical indices s and s’ of on-sites tensors \(A\) (and \(A^\dagger\)) are left uncontracted and given in the following order:
s0 s1 s2 s3