Tools /
## MpReflectThe ## Synopsis
## Options
show help message
`--force` overwrite the output file, if it exists
## DescriptionThe If the output file already exists, then ## Examples- Calculate the reflection of
`psi1` , and save it as`psi2` `mp-reflect psi1 psi2` If`psi2` already exists, then this will fail with an error, leaving the existing file`psi2` untouched. To force overwriting`psi2` , add the`-f` option.
## Implementation notesGiven an MPS, that may be a unit cell of an iMPS, or a finite MPS, or an IBC MPS, {$$A_1^{s_1} A_2^{s_2} \cdots A_N^{s_N}$$} the spatial reflection is given by the MPS sequence {$$A_N^{s_N T} A_{N-1}^{s_{N-1}T} \cdots A_1^{s_1 T}$$} That is, transpose each A-matrix, and reverse the ordering. With good quantum numbers, the transpose operation needs to be modified. This is because the matrix elements of an operator that transforms irreducibly under some symmetry satisfy a quantum number constraint, for example with particle number symmetry suppose we have a particular A-matrix {$A^1$} representing a local particle state. Then the non-zero matrix elements {$A_{nm}^1$} satisfy the quantum number constraint {$n=m+1$}. However if we take the transpose, {$A^{1T}$} then it doesn't satisfy any more this sum rule, since we now have {$(A^{1T})_{nm}$} with {$n=m-1$}. To get around this, we perform the 'flip transposition', which is a flip of the quantum numbers in the auxiliary basis of the MPS, {$m \rightarrow m' = -m$}, {$n \rightarrow n' = -n$}. Now we have {$n' = m'+1$}, and the A-matrix has the correct symmetry. In practice, this is implemented in the toolkit as |

Page last modified on July 25, 2016, at 07:10 PM