Matrix Product Toolkit | Tools / MpIBcCreate

Create an IBC wavefunction from one or two boundary infinite wavefunctions.

Synopsis

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

Options

--help

Show help message.

-o, --output

Output wavefunction filename (required).

-f, --force

Force overwriting the output file if it already exists.

-H, --Hamiltonian

The operator the use for the Hamiltonian (if unspecified, use wavefunction attribute Hamiltonian of psi). Only required if minimising the energy.

-q, --quantumnumber

Shift the right boundary by this quantum number (default identity).

--tol

Error tolerance for the eigensolver when minimising the energy with respect to the central matrix (default 1e-15).

--gmrestol

Error tolerance for the GMRES algorithm for solving the left and right block Hamiltonians (default 1e-13).

--streaming

Store the left and right boundary wavefunctions by references to the input files.

--no-streaming

Store the left and right boundary wavefunctions by writing them to the output files (default).

--random

Use a random central matrix between the two boundaries instead of minimising the energy.

--boundary-lambda

Use left boundary’s lambda matrix instead of solving for the lambda matrix (will do this anyway if only one input wavefunction is specified).

-v, --verbose

Increase verbosity.

Description

This tool creates an infinite boundary condition (IBC) wavefunction of the form {$$|\Psi\rangle = \cdots A_L^{s_{-3}} A_L^{s_{-2}} A_L^{s_{-1}} \Lambda A_R^{s_0} A_R^{s_1} A_R^{s_2} \cdots,$$} where {$A_L$} and {$A_R$} are the left- and right-orthogonal forms of the same or two different wavefunctions.

If {$A_L$} and {$A_R$} are from the same wavefunction, then the central matrix {$\Lambda$} can be obtained from the {$\Lambda$} matrix of either boundary.

However, if {$A_L$} and {$A_R$} are from two different wavefunctions, this {$\Lambda$} matrix needs to be solved for: this is done by minimising the energy with respect to some Hamiltonian specified by -H, or as the wavefunction attribute of the left boundary. (If we are using a lattice with quantum numbers, we may have to adjust the quantum number shift of the right boundary with -q to make sure the two boundaries join together properly).

The output wavefunction will have a zero-site window containing just the central matrix {$\Lambda$}.