apply_op_itrunc() [2/2]

SRDef syten::MPS::apply_op_itrunc	(	State &	a,
		Operator const &	op,
		Truncation	trunc,
		bool const	relax = true,
		bool const	final_rightnorm = true
	)

Applies the MPO op to the MPS a, immediately truncating during the application.

Parameters

[in,out]	a	the MPS to which the operator is applied
[in]	op	the MPO which is applied to the state
[in]	trunc	Truncation specification
[in]	relax	whether to relax the truncation spec during the initial left-to-right sweep
[in]	final_rightnorm	if false, don't do a right-normalisation at the end

Returns

the error incurred during truncation. Only a rough estimate.

Steps taken:

• Right-normalise the state without truncation
• On the first site, contract the MPS and MPO, then left-normalise using a (relaxed) truncation spec.
• On every other site, multiply the left-over truncator from the previous site into the left isometry before contracting MPO and MPS components on that site, then normalise with the same procedure as on the first site.
• On the last site, do not normalise the state.
• Right-normalise and truncate with the supplied truncation specification.

Remarks

In principle, it would be possible to insert further SVDs, in particular on the two legs of (FAW) to the right. The singular value tensors could then be multiplied into the splitting coming from the right and another SVD could work on the splitting tensor instead of the whole tensor. However, this does require three SVDs of comparable cost instead of a single one, so it’s unlikely to be any faster.

References syten::MPS::Operator::dIdx, syten::MPS::State::dropUnmatched(), syten::genCombinator(), syten::genFuse(), syten::genSplit(), syten::MPS::Operator::lIdx, syten::MPS::State::lIdx, syten::MPS::State::lInt, syten::Truncation::maxBlocksize, syten::Truncation::maxStates, syten::MPS::State::maybeCache(), norm(), syten::MPS::Operator::rIdx, syten::MPS::State::rIdx, syten::MPS::State::rightnorm(), syten::MPS::State::rInt, syten::MPS::State::size(), syten::SVD::svd(), SYTEN_ASSERT, syten::Truncation::threshold, syten::MPS::Operator::uIdx, syten::MPS::State::uInt, and syten::validateTensorEdge().

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