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Algorithms for entanglement renormalization
We describe an iterative method to optimize the multiscale entanglement renormalization ansatz for the low-energy subspace of local Hamiltonians on a D -dimensional lattice. For translation-invariant
Tensor Network Renormalization.
We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a
Tensor Network States and Geometry
Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different
Tensor Network Renormalization Yields the Multiscale Entanglement Renormalization Ansatz.
TLDR
This work shows how to build a multiscale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian H by applying the Euclidean time evolution operator e(-βH) for infinite β and extends the MERA formalism to classical statistical systems.
Entanglement Renormalization and Wavelets.
TLDR
This work employs Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrates that these states correspond to instances of the multiscale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems.
Class of highly entangled many-body states that can be efficiently simulated.
We describe a quantum circuit that produces a highly entangled state of N qubits from which one can efficiently compute expectation values of local observables. This construction yields a variational
Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
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
Frustrated antiferromagnets with entanglement renormalization: ground state of the spin-1/2 Heisenberg model on a kagome lattice.
TLDR
Entanglement renormalization techniques are applied to numerically investigate the ground state of the spin-1/2 Heisenberg model on a kagome lattice and the best approximation to the groundstate is found to be a valence bond crystal with a 36-site unit cell.
Scaling of entanglement entropy in the (branching) multiscale entanglement renormalization ansatz
We investigate the scaling of entanglement entropy in both the multiscale entanglement renormalization ansatz (MERA) and in its generalization, the branching MERA. We provide analytical upper bounds
Quantum Criticality with the Multi-scale Entanglement Renormalization Ansatz
The goal of this manuscript is to provide an introduction to the multi-scale entanglement renormalization ansatz (MERA) and its application to the study of quantum critical systems. Only systems in
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