0000000000003170

AUTHOR

Kai Phillip Schmidt

0000-0002-8278-8238

Entanglement continuous unitary transformations

Continuous unitary transformations are a powerful tool to extract valuable information out of quantum many-body Hamiltonians, in which the so-called flow equation transforms the Hamiltonian to a diagonal or block-diagonal form in second quantization. Yet, one of their main challenges is how to approximate the infinitely-many coupled differential equations that are produced throughout this flow. Here we show that tensor networks offer a natural and non-perturbative truncation scheme in terms of entanglement. The corresponding scheme is called "entanglement-CUT" or eCUT. It can be used to extract the low-energy physics of quantum many-body Hamiltonians, including quasiparticle energy gaps. We…

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Fine Grained Tensor Network Methods.

We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine-grain the physical degrees of freedom, i.e., decompose them into more fundamental units which, after a suitable coarse-graining, provide the original ones. Thanks to this procedure, the original lattice with high connectivity is transformed by an isometry into a simpler structure, which is easier to simulate via usual tensor network methods. In particular this enables the use of standard schemes to contract infinite 2d tensor networks - such as Corner Transfer Matrix Renormalization schemes - which are more involved on complex lattice structu…

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