Recent zbMATH articles in MSC 94A24https://zbmath.org/atom/cc/94A242024-03-13T18:33:02.981707ZWerkzeugA new entanglement monotone based on min-relative entropyhttps://zbmath.org/1528.810312024-03-13T18:33:02.981707Z"Cui, Shijie"https://zbmath.org/authors/?q=ai:cui.shijie"Li, Junqing"https://zbmath.org/authors/?q=ai:li.junqing"Huang, Li"https://zbmath.org/authors/?q=ai:huang.liSummary: Quantum relative entropy has been studied extensively, and many forms have been derived due to different parameters. Maximum relative entropy and minimum relative entropy are obtained by taking specific conditions for parameters. Our goal in this paper is to propose a new bipartite entanglement monotone based on minimum relative entropy of any bipartite quantum entanglement state. We also demonstrate that entanglement monotone satisfies some basic properties as an entanglement measure.Entanglement bipartitioning and tree tensor networkshttps://zbmath.org/1528.810432024-03-13T18:33:02.981707Z"Okunishi, Kouichi"https://zbmath.org/authors/?q=ai:okunishi.kouichi"Ueda, Hiroshi"https://zbmath.org/authors/?q=ai:ueda.hiroshi"Nishino, Tomotoshi"https://zbmath.org/authors/?q=ai:nishino.tomotoshiSummary: We propose the entanglement bipartitioning approach to design an optimal network structure of the tree tensor network (TTN) for quantum many-body systems. Given an exact ground-state wavefunction, we perform sequential bipartitioning of spin-cluster nodes so as to minimize the mutual information or the maximum loss of the entanglement entropy associated with the branch to be bipartitioned. We demonstrate that entanglement bipartitioning of up to 16 sites gives rise to nontrivial tree network structures for \(S = 1/2\) Heisenberg models in one and two dimensions. The resulting TTNs enable us to obtain better variational energies, compared with standard TTNs such as the uniform matrix product state and perfect binary tree tensor network.