What you know you can't explain, but you feel it. You've felt it your entire life, that there's something wrong with the world. You don't know what it is, but it's there, like a splinter in your mind, driving you mad.

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