# Entanglement Renormalization of Thermofield Double States.

@article{Lin2021EntanglementRO, title={Entanglement Renormalization of Thermofield Double States.}, author={Cheng-Ju Lin and Zhi Li and Timothy H. Hsieh}, journal={Physical review letters}, year={2021}, volume={127 8}, pages={ 080602 } }

Entanglement renormalization is a method for "coarse graining" a quantum state in real space, with the multiscale entanglement renormalization ansatz as a notable example. We obtain an entanglement renormalization scheme for finite-temperature (Gibbs) states by applying the multiscale entanglement renormalization ansatz to their canonical purification, the thermofield double state. As an example, we find an analytically exact renormalization circuit for a finite-temperature two-dimensional…

## One Citation

RG Flows and Thermofield-Double States in Holography

- Physics
- 2021

In this article, we consider a Renormalization Group flow of the ThermofieldDouble state in a UV-complete description of Holography, by introducing a relevant deformation to the N = 4 super…

## References

SHOWING 1-10 OF 56 REFERENCES

Entanglement renormalization.

- Physics, MedicinePhysical review letters
- 2007

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, and calculations unveil that ground state entanglement in extended quantum systems is organized in layers corresponding to different length scales.

Entanglement renormalization and topological order.

- Physics, MedicinePhysical review letters
- 2008

The case of Kitaev's toric code is analyzed in detail and shown to possess a remarkably simple MERA description leading to distillation of the topological degrees of freedom at the top of the tensor network.

Entanglement renormalization in two spatial dimensions.

- Physics, MedicinePhysical review letters
- 2009

A calculation of the energy gap shows that it scales as 1/L at the critical point, and a scheme for entanglement renormalization capable of addressing large two-dimensional quantum lattice systems is proposed and tested.

Tensor Network Renormalization Yields the Multiscale Entanglement Renormalization Ansatz.

- Physics, MedicinePhysical review letters
- 2015

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.

Structure of quantum entanglement at a finite temperature critical point

- Physics
- 2019

We propose a scheme to characterize long-range quantum entanglement close to a finite temperature critical point using tripartite entanglement negativity. As an application, we study a model with…

Entanglement renormalization for chiral topological phases

- PhysicsPhysical Review B
- 2019

We considered the question of applying the multiscale entanglement renormalization ansatz (MERA) to describe chiral topological phases. We defined a functional for each layer in the MERA, which…

Anomalies and entanglement renormalization

- Physics
- 2017

We study 't Hooft anomalies of discrete groups in the framework of (1+1)-dimensional multiscale entanglement renormalization ansatz states on the lattice. Using matrix product operators, general…

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…

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…

Variational Thermal Quantum Simulation via Thermofield Double States.

- Physics, MedicinePhysical review letters
- 2019

This work demonstrates that thermal states of the 1D classical Ising model at any temperature can be prepared with perfect fidelity using L/2 iterations, where L is system size.