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MpIBcSplice

Create an IBC wavefunction by joining two IBC wavefunctions together.

Synopsis

mp-ibc-splice [options] <psi-left> <psi-right> -o <psi-out>

Options

--help

-o, --output

--tol

-n, --nleft

--nright

-v, --verbose

Description

This 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 --tol.

Alternatively, we can set the number of sites to incorporate into each window with --nleft and --nright. Although care should be taken when incorporating few sites, since the window of an IBC wavefunction will affect the state at the boundary within a distance on the order of the correlation length, and incorporating too few sites will result in distorting the wavefunction between the two windows.