2009/03/31 by Luca Tagliacozzo, L. Tagliacozzo, Glen Evenbly +3 · 13 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #Quantum many-body systems #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.80.235127
published as Phys. Rev. B 80, 235127 (2009) · Major rewrite, new version published in Phys. Rev. B with highly improved numerical results for the scaling of the entropies and several new sections. The manuscript has now 19 pages and 30 Figures
openalex publication_date 2009/12/18 · arxiv created 2009/12/21 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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 quasiexact results in systems with sizes well beyond the reach of exact diagonalization techniques. We describe an algorithm to approximate the ground state of a local Hamiltonian on a L\ifmmode×\else\texttimes\fiL 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 analyze 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.