# Entanglement renormalization.

@article{Vidal2007EntanglementR, title={Entanglement renormalization.}, author={Guifr{\'e} Vidal}, journal={Physical review letters}, year={2007}, volume={99 22}, pages={ 220405 } }

We propose a real-space renormalization group (RG) transformation for quantum systems on a D-dimensional lattice. The transformation partially disentangles a block of sites before coarse-graining it into an effective site. Numerical simulations with the ground state of a 1D lattice at criticality show that the resulting coarse-grained sites require a Hilbert space dimension that does not grow with successive RG transformations. As a result we can address, in a quasi-exact way, tens of thousands…

## 441 Citations

### Real-space renormalization yields finite correlations.

- PhysicsPhysical review letters
- 2010

It is shown that real-space renormalization generates states which can be encoded with local effective degrees of freedom, and MERA states form an efficiently contractible class of PEPS that obey the area law for the entanglement entropy.

### Implicitly disentangled renormalization

- Computer Science, Physics
- 2017

This work proposes a new implementation of real-space renormalization group (RG) transformations for quantum states on a lattice that only uses operators that act locally within each block, such that the use of disentanglers acting across block boundaries is not required.

### Entanglement Renormalization of Thermofield Double States.

- PhysicsPhysical review letters
- 2021

An analytically exact renormalization circuit for a finite-temperature two-dimensional toric code that maps it to a coarse-grained system with a renormalized higher temperature, thus explicitly demonstrating its lack of topological order is found.

### Entanglement and correlations in the continuous multi-scale entanglement renormalization ansatz

- Physics
- 2017

A bstractWe investigate the entanglement structure of the continuous multi-scale entanglement renormalization ansatz (cMERA) [Haegeman et al., Phys. Rev. Lett.110 (2013) 100402] for ground states of…

### Entanglement Renormalization and Holography

- Physics
- 2012

We show how recent progress in real space renormalization group methods can be used to define a generalized notion of holography inspired by holographic dualities in quantum gravity. The…

### Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator.

- PhysicsPhysical review letters
- 2019

It is demonstrated that the cMERA circuit can potentially be realized in existing analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical lattice with light-induced spin-orbit coupling.

### Quantum Circuit Approximations and Entanglement Renormalization for the Dirac Field in 1+1 Dimensions

- Physics, Computer ScienceCommunications in Mathematical Physics
- 2021

This work uses multiresolution analysis from wavelet theory to obtain an approximation scheme and to implement entanglement renormalization in a natural way, which could be a starting point for constructing quantum circuit approximations for more general conformal field theories.

### Rigorous free fermion entanglement renormalization from wavelet theory

- Physics, Computer Science
- 2017

Entanglement renormalization schemes are constructed which provably approximate the ground states of non-interacting fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice and it is shown how the error in the approximation can be controlled without ever performing a variational optimization.

### Bifurcation in entanglement renormalization group flow of a gapped spin model

- Physics
- 2014

We study entanglement renormalization group transformations for the ground states of a spin model, called cubic code model $H_A$ in three dimensions, in order to understand long-range entanglement…

### Tensor Renormalization Group for interacting quantum fields

- PhysicsQuantum
- 2021

We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. It is based on the Tensor Renormalization Group (TRG) protocol,…

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