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Note that the local dimension d of the original lattice, in which the Hamiltonian is defined, is usually smaller than the local dimension χ of a coarse-grained site. In this case the computational cost to compute ascending/descending superoperators and environments for the first layer of the MERA is smaller than for the higher layers.
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Note that the local dimension d of the original lattice, in which the Hamiltonian is defined, is usually smaller than the local dimension χ of a coarse-grained site. In this case the computational cost to compute ascending/descending superoperators and environments for the first layer of the MERA is smaller than for the higher layers.
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Note that in some cases a fermionic swap gate can only be absorbed in a later stage of the contraction, i.e., not necessarily at the beginning.
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In this example we study the noninteracting case in order to be able to compare with the exact result. (No exact results are available for the interacting case for large systems). The energy as a function of χ behaves similarly in the interacting case as in the noninteracting case, but with a slower convergence for intermediate interaction strengths V∼1 where the amount of entanglement in the system is large (cf. Fig.).
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In this example we study the noninteracting case in order to be able to compare with the exact result. (No exact results are available for the interacting case for large systems). The energy as a function of χ behaves similarly in the interacting case as in the noninteracting case, but with a slower convergence for intermediate interaction strengths V∼1 where the amount of entanglement in the system is large (cf. Fig.).
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