Simulation of twodimensional quantum systems using a tree tensor network that exploits the entropic area law
Abstract
This work explores the use of a tree tensor network ansatz to simulate the ground state of a local Hamiltonian on a twodimensional 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×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 analyze the scaling of the groundstate 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 .
 Publication:

Physical Review B
 Pub Date:
 December 2009
 DOI:
 10.1103/PhysRevB.80.235127
 arXiv:
 arXiv:0903.5017
 Bibcode:
 2009PhRvB..80w5127T
 Keywords:

 64.60.ae;
 64.60.an;
 64.60.De;
 65.40.gd;
 Renormalizationgroup theory;
 Finitesize systems;
 Statistical mechanics of model systems;
 Entropy;
 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Statistical Mechanics
 EPrint:
 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