Notation for the various matrices and their dimensions:
- {$A^s_{ij}$}: an A-matrix, representing a matrix product wavefunction. {$|s\rangle$} is the local basis. Usually, the {$ij$} indices are suppressed.
- {$M^{s's}_{\alpha'\alpha}$}: an M-matrix, representing a matrix product operator. {$|s'\rangle \langle s|$} is the local basis.
- {$E^\alpha_{ij}, \; F^\alpha, \; \ldots$}: an E-matrix, representing the local matrix elements of an operator. Again, the {$ij$} indices are usually suppressed.
- {$\alpha,\beta,\ldots$}: these indices run over the matrix basis of a matrix product operator, and the local basis of an E-matrix.
- {$i,j,\ldots$}: these indices run over the matrix basis of an A-matrix and an E-matrix.
- {$L$}: lattice size
- {$m$}: matrix dimension of an A-matrix. Equal to the number of states in DMRG. {$\mathrm{dim}\{|i\rangle\}$}
- {$d$}: dimension of the local basis of an A-matrix, {$\mathrm{dim}\{|s\rangle\}$}
- {$M$}: matrix dimension of an M-matrix, {$\mathrm{dim}\{|\alpha\rangle\}$}. In the superblock representation, this is the number of terms of the form {$L_1 \otimes R_1 + L_2 \otimes R_2 \cdots$}
- {$D$}: dimension of the local basis of an M-matrix. Equal to {$d^2$}, not used often.