利用熵面积定律的树形张量网络模拟二维量子系统
Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
摘要：
本文利用树型张量网络模拟了二维晶格上局部哈密顿量的基态。通过利用熵面积定律，树张量网络分析器似乎在尺寸远远超出精确对角化技术范围的系统中产生准精确结果。我们描述了一个算法来近似局部哈密顿的基态的L倍L格与环面拓扑。对于L={4，6，8}得到了精确的结果，而对于较大的晶格得到了近似的结果。作为该方法的一个应用，我们分析了基态纠缠熵在量子临界点的标度性。我们确认存在一个积极的添加剂常数的面积法半环面。我们还发现了一个对数加法修正的熵面积法的方块。半个环面的单拷贝纠缠揭示了对面积定律的类似修正，进一步的项与1/L成比例。
英文摘要：
This work explores the use of a tree tensor network ansatz to simulate the ground state of a local Hamiltonian on a two-dimensional lattice. By exploiting the entropic area law, the tree tensor network ansatz seems to produce quasi-exact results in systems with sizes well beyond the reach of exact diagonalisation techniques. We describe an algorithm to approximate the ground state of a local Hamiltonian on a L times L lattice with the topology of a torus. Accurate results are obtained for L={4,6,8}, whereas approximate results are obtained for larger lattices. As an application of the approach, we analyse the scaling of the ground state entanglement entropy at the quantum critical point of the model. We confirm the presence of a positive additive constant to the area law for half a torus. We also find a logarithmic additive correction to the entropic area law for a square block. The single copy entanglement for half a torus reveals similar corrections to the area law with a further term proportional to 1/L.
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