# Simulation of interacting fermions with entanglement renormalization

@article{Corboz2010SimulationOI, title={Simulation of interacting fermions with entanglement renormalization}, author={Philippe Corboz and Glen Evenbly and F. Verstraete and Guifr{\'e} Vidal}, journal={Physical Review A}, year={2010}, volume={81} }

We propose an algorithm to simulate interacting fermions on a two-dimensional lattice. The approach is an extension of the entanglement renormalization technique [Phys. Rev. Lett. 99, 220405 (2007)] and the related multiscale entanglement renormalization ansatz. Benchmark calculations for free and interacting fermions on lattices ranging from 6×6 to 162×162 sites with periodic boundary conditions confirm the validity of this proposal. © 2010 The American Physical Society

## 67 Citations

### Entanglement renormalization for quantum fields in real space.

- PhysicsPhysical review letters
- 2013

This work shows how to construct renormalization group (RG) flows of quantum field theories in real space, as opposed to the usual Wilsonian approach in momentum space, and argues that the full power of the construction should emerge in the case of interacting theories.

### Causal structure of the entanglement renormalization ansatz

- Physics
- 2011

We show that the multiscale entanglement renormalization ansatz (MERA) can be reformulated in terms of a causality constraint on discrete quantum dynamics. This causal structure is that of de Sitter…

### Simulation of strongly correlated fermions in two spatial dimensions with fermionic projected entangled-pair states

- Physics
- 2010

We explain how to implement, in the context of projected entangled-pair states (PEPSs), the general procedure of fermionization of a tensor network introduced in P. Corboz and G. Vidal, Phys. Rev. B…

### 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.

### Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems

- Physics
- 2010

In this paper, we review the properties of homogeneous multiscale entanglement renormalization ansatz (MERA) to describe quantum critical systems. We discuss in more detail our results for…

### Algorithms for Entanglement Renormalization: Boundaries, Impurities and Interfaces

- Physics
- 2014

We propose algorithms, based on the multi-scale entanglement renormalization ansatz, to obtain the ground state of quantum critical systems in the presence of boundaries, impurities, or interfaces.…

### cMERA for Interacting Fields

- Physics
- 2016

We upgrade cMERA to a systematic variational ansatz and develop techniques for its application to interacting quantum field theories in arbitrary spacetime dimensions. By establishing a…

### 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.

### Foundations and Applications of Entanglement Renormalization

- Physics
- 2010

Understanding the collective behavior of a quantum many-body system, a system composed of a large number of interacting microscopic degrees of freedom, is a key aspect in many areas of contemporary…

### Advances on tensor network theory: symmetries, fermions, entanglement, and holography

- Physics
- 2014

This is a short review on selected theory developments on tensor network (TN) states for strongly correlated systems. Specifically, we briefly review the effect of symmetries in TN states, fermionic…

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