Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
By Luca Tagliacozzo, Glen Evenbly, Guifré Vidal. 2009
209 citations recorded by the source corpus.
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×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 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.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/7550f5a4f6e2c2e92ddac1eeb73b0c36fa89349c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Marcello Dalmonte
- A. Nahum
- Peter Zoller
- Simone Montangero
- B. Skinner
- David Gross
- Steven T. Flammia
- Frank Verstraete
In Atomic and Molecular Physics, and Optics
- Marcello Dalmonte
- Simone Montangero
- Peter Zoller
- A. Nahum
- Frank Verstraete
- J. Ruhman
- B. Skinner
- Andrew J. Daley
Citations in the corpus
- Lattice gauge theory simulations in the quantum information era (2016, unknown): “Finally, one can also build hierarchical structures which are intimately related to the real space renormalization group procedure, such as Tree Tensor Networks (TTN) [74–76] and Multi-scale Entanglement Renormalization Ansatz (MERA) [77].”
- Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory (2020, background): “Tree tensor networks are also interesting quite apart from the connection to the all-to-all circuit [56–65].”
- Efficient quantum state tomography. (2010, methodology): “Combinations of our techniques can be used to reconstruct other classes of states, such as tree tensor networks [36] and multiscale entanglement renormalization ansatz (MERA) states [37], for which efficient heuristics for minimizing local Hamiltonians are available.”
- Neural Network Renormalization Group (2018, background): “spired network structure can nevertheless be generalized by following considerations in tensor network architecture design [75, 76].”
- Simulating lattice gauge theories within quantum technologies (2019, methodology): “In particular, the projector is built as hierarchical tensor networks such as the MERA [99] and the Tree Tensor Network [100].”