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## MpApplyOptThe Matrix Product Toolkit version HEAD-0.7.4.0 (subversion tree rev 661M) Compiled on Jun 25 2007 at 22:43:45 usage: mp-apply-opt [options] <operator> <rhs> <psi> Allowed options: --help show this help message -2 [ --two-site ] modify 2 neighboring sites at once --min-states arg Minimum number of states to keep [default 1] -m [ --max-states ] arg Maximum number of states to keep [default 10000] -r [ --trunc ] arg Cutoff truncation error per site [default 0] -d [ --eigen-cutoff ] arg Cutoff threshold for density matrix eigenvalues [default -1] -f [ --mix-factor ] arg Mixing coefficient for the density matrix [default 0.01] -s [ --sweeps ] arg Number of half-sweeps to perform [default 2] --a2 arg Use this pre-computed value of <rhs|adjoint(A)*A|rhs> to speed up the residual calculation --no-resid Don't calculate the final residual norm The usual options for truncating the basis all work. In this case, they are applied By default (unless the Calculating the residual norm is an expensive operation however, because it requires knowing {$\langle \psi|A^\dagger A|\psi\rangle$}. If this value is already known, then it can instead be supplied with the If the guess vector is not expected to be very good, then adding a mixing factor works extremely well. Once the guess vector is a fairly good approximation, then it appears that the 2-site algorithm with no mixing factor produces an optimal solution very quickly. ## ExamplesRemember that we always require an existing wavefunction to use as a guess vector, and this Suppose we have a poor quality guess wavefunction, and we want to optimize {$|guess\rangle = lattice:A |input\rangle$}. mp-apply-opt -m 150 -f 0.001 lattice:A input guess Once {$|guess\rangle$} is reasonably good, then the 2-site algorithm with no mixing works extremely well, and seems to produce an essentially mp-apply-opt -m 150 -f 0 -2 --a2=7.32879847982 lattice:A input guess Here, we used the value of {$\langle input | A^\dagger A |input \rangle$} that was given by the previous run of ## NotesIt would be nice to have an option to do one half-sweep with a mixing factor, and then the return half-sweep with the 2-site algorithm. This should be added sometime. Doing just a single half-sweep with In fact, the way the truncations are done is not as precise as we would like. Relative truncation means each local operation is done relative to the local norm at each iteration. In fact it would be better to use the computed The residual norm calculation will fail for a non-Abelian symmetry where the operator {$A$} is not a scalar. This isn't easy to fix, but it should be possible to supply the correct value with ## See Also |

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