Reduced Density Matrices¶
-
ctm.generic.rdm.
rdm1x1
(coord, state, env, verbosity=0)[source]¶ - Parameters
- Returns
1-site reduced density matrix with indices \(s;s'\)
- Return type
torch.tensor
Computes 1-site reduced density matrix \(\rho_{1x1}\) centered on vertex
coord
by contracting the following tensor network:C--T-----C | | | T--A^+A--T | | | 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.generic.rdm.
rdm1x2
(coord, ipeps, env, verbosity=0)[source]¶ - Parameters
- Returns
2-site reduced density matrix with indices \(s_0s_1;s'_0s'_1\)
- Return type
torch.tensor
Computes 2-site reduced density matrix \(\rho_{1x2}\) of a vertical 1x2 subsystem using following strategy:
compute four individual corners
construct upper and lower half of the network
contract upper and lower halt to obtain final reduced density matrix
C--T------------------C = C2x2_LU(coord)--------C1x2(coord) | | | | | T--A^+A(coord)--------T C2x2_LD(coord+(0,1))--C1x2(coord+0,1)) | | | T--A^+A(coord+(0,1))--T | | | C--T------------------C
The physical indices s and s’ of on-sites tensors \(A\) (and \(A^\dagger\)) at vertices
coord
,coord+(0,1)
are left uncontracted
-
ctm.generic.rdm.
rdm2x1
(coord, ipeps, env, verbosity=0)[source]¶ - Parameters
- Returns
2-site reduced density matrix with indices \(s_0s_1;s'_0s'_1\)
- Return type
torch.tensor
Computes 2-site reduced density matrix \(\rho_{2x1}\) of a horizontal 2x1 subsystem using following strategy:
compute four individual corners
construct right and left half of the network
contract right and left halt to obtain final reduced density matrix
C--T------------T------------------C = C2x2_LU(coord)--C2x2(coord+(1,0)) | | | | | | T--A^+A(coord)--A^+A(coord+(1,0))--T C2x1_LD(coord)--C2x1(coord+(1,0)) | | | | C--T------------T------------------C
The physical indices s and s’ of on-sites tensors \(A\) (and \(A^\dagger\)) at vertices
coord
,coord+(1,0)
are left uncontracted
-
ctm.generic.rdm.
rdm2x2
(coord, ipeps, env, verbosity=0)[source]¶ - Parameters
- Returns
4-site reduced density matrix with indices \(s_0s_1s_2s_3;s'_0s'_1s'_2s'_3\)
- Return type
torch.tensor
Computes 4-site reduced density matrix \(\rho_{2x2}\) of 2x2 subsystem specified by the vertex
coord
of its upper left corner using strategy:compute four individual corners
construct upper and lower half of the network
contract upper and lower half to obtain final reduced density matrix
C--T------------------T------------------C = C2x2_LU(coord)--------C2x2(coord+(1,0)) | | | | | | T--A^+A(coord)--------A^+A(coord+(1,0))--T C2x2_LD(coord+(0,1))--C2x2(coord+(1,1)) | | | | T--A^+A(coord+(0,1))--A^+A(coord+(1,1))--T | | | | C--T------------------T------------------C
The physical indices s and s’ of on-sites tensors \(A\) (and \(A^\dagger\)) at vertices
coord
,coord+(1,0)
,coord+(0,1)
, andcoord+(1,1)
are left uncontracted and given in the same order:s0 s1 s2 s3