Point group: square lattice¶
Functions symmetrizing (rank-5) on-site tensor by projecting into one of the irreps of the point-group of square lattice \(C_{4v}\). All functions assume following index convention of on-site tensor:
u s
|/
l--A--r <=> A[s,u,l,d,r]
|
d
where first index, s, is physical.
- groups.pg.make_c4v_symm(A, irreps=['A1'])[source]¶
- Parameters:
A (torch.Tensor) – on-site tensor
irreps (list(str)) – choice of irreps from
'A1'
,'A2'
,'B1'
, or'B2'
- Returns:
C4v symmetrized tensor A
- Return type:
torch.Tensor
Sum any combination of projections on real \(C_{4v}\) irreps \(A_1, A_2, B_1, B_2\). List of irreps is converted to a set (no repeated elements) and the projections are then summed up.
- groups.pg.make_c4v_symm_A1(A)[source]¶
- Parameters:
A (torch.Tensor) – on-site tensor
- Returns:
projection of A to \(A_1\) irrep
- Return type:
torch.Tensor
Project on-site tensor A on \(A_1\) irrep of \(C_{4v}\) group.
- groups.pg.make_c4v_symm_A2(A)[source]¶
- Parameters:
A (torch.Tensor) – on-site tensor
- Returns:
projection of A to \(A_2\) irrep
- Return type:
torch.Tensor
Project on-site tensor A on \(A_2\) irrep of \(C_{4v}\) group.
- groups.pg.make_c4v_symm_B1(A)[source]¶
- Parameters:
A (torch.Tensor) – on-site tensor
- Returns:
projection of A to \(B_1\) irrep
- Return type:
torch.Tensor
Project on-site tensor A on \(B_1\) irrep of \(C_{4v}\) group.
- groups.pg.make_c4v_symm_B2(A)[source]¶
- Parameters:
A (torch.Tensor) – on-site tensor
- Returns:
projection of A to \(B_2\) irrep
- Return type:
torch.Tensor
Project on-site tensor A on \(B_2\) irrep of \(C_{4v}\) group.