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derivative that we set to $latex {0}&fg=000000$ and solve.https://windowsontheory.org/wp-content/uploads/2018/12/note39x.pngnote39xThe Langrangian $latex {{\langle \psi| H | \psi \rangle} - \lambda {\langle \psi ||\psi \rangle}}&fg=000000$ as a tensor network.https://windowsontheory.org/wp-content/uploads/2018/12/note37x.pngnote37xThe quadratic form $latex {\langle \psi| H | \psi \rangle}&fg=000000$https://windowsontheory.org/wp-content/uploads/2018/12/note36x.pngnote36xInput $latex {1}&fg=000000$D Hamiltonian is of the particular product form.https://windowsontheory.org/wp-content/uploads/2018/12/note33x.pngnote33xRepresentation power of MPS increases with bond dimension D.https://windowsontheory.org/wp-content/uploads/2018/12/note21x.pngnote21xA matrix product state.https://windowsontheory.org/wp-content/uploads/2018/12/note20x.pngnote20xhttps://windowsontheory.org/wp-content/uploads/2018/12/note16x.pngnote16xMatrix inner product 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to convince E. Abakoumov. 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