Tools /
## MpIBcSpliceCreate an IBC wavefunction by joining two IBC wavefunctions together. ## Synopsis
## Options
Show help message.
`--output` Filename for the output wavefunction.
Tolerance in the squared Frobenius norm in the difference of the center matrix and the corresponding translation-invariant fixed point: this will determine how many sites to add between the two windows. (default `1e-10` ).
`--nleft` The number of unit cells to add to the left window from the middle boundary (alternative to `--tol` ).
The number of unit cells to add to the right window from the middle boundary (if `--nleft` is specified and `--nright` is not, will just use the value from `--nleft` ).
`--verbose` Increase verbosity.
## DescriptionThis tool takes two IBC wavefunctions {$$|\Psi_1\rangle = \cdots AAAW_1^1W_2^1W_3^1\cdots W_{N_1}^1BBB\cdots, \qquad |\Psi_2\rangle = \cdots BBBW_1^2W_2^2W_3^2\cdots W_{N_2}^2CCC\cdots,$$} and splices them together to create a single IBC wavefunction with a larger window: {$$|\Psi\rangle = \cdots AAA\tilde{W}_1\tilde{W}_2\tilde{W}_3\cdots \tilde{W}_NCCC\cdots,$$} where {$$\tilde{W}_1\tilde{W}_2\cdots \tilde{W}_N = W_1^1W_2^1\cdots W_{N_1}^1\underbrace{BB\cdots BB}_{N_L+N_R~\text{sites}}W_1^2W_2^2\cdots W_{N_2}^2.$$} The number of sites {$N_L+N_R$} to add between the two windows is determined by progressively incorporating sites into the left window (and similarly for the right window), moving the orthogonality center matrix {$\Lambda$} to the edge of the added sites:
{$$W_1^1W_2^1\cdots W_{N_1}^1 \tilde{B}^1_1 \tilde{B}^1_2 \cdots \tilde{B}^1_{N_L} \Lambda.$$}
Here, the {$\tilde{B}^1_i$} matrices will not be exactly the same as the translation-invariant counterpart {$B$}, since we have pulled {$\Lambda$} through them.
We do this until the squared Frobenius norm of the difference of this {$\Lambda$} with the translation-invariant counterpart {$\Lambda_0$} is below some tolerance set by Alternatively, we can set the number of sites to incorporate into each window with |

Page last modified on October 20, 2023, at 04:14 AM