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

@article{Ors2014AdvancesOT, title={Advances on tensor network theory: symmetries, fermions, entanglement, and holography}, author={Rom{\'a}n Or{\'u}s}, journal={The European Physical Journal B}, year={2014}, volume={87}, pages={1-18} }

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 TNs, the calculation of entanglement Hamiltonians from projected entangled pair states (PEPS), and the relation between the multi-scale entanglement renormalization ansatz (MERA) and the AdS/CFT or gauge/gravity duality. We stress the role played by entanglement in the emergence of several physical…

## 97 Citations

### Tensor Networks , Matrix Product States and Density Matrix Renormalization Group

- Computer Science
- 2018

DMRG, due to White (1992, 1993) [Whi92, Whi93], is arguably the most successful heuristic for this problem and is described in the language of tensor networks and MPS.

### Tensor networks for complex quantum systems

- PhysicsNature Reviews Physics
- 2019

This Review revisits the main tensor network structures, key ideas behind their numerical methods and their application in fields beyond condensed matter physics.

### Discrete gravity on random tensor network and holographic Rényi entropy

- Computer ScienceJournal of High Energy Physics
- 2017

The boundary many-body quantum state |Ψ〉 is constructed using random tensor networks as the holographic mapping, applied to the Wheeler-deWitt wave function of bulk Euclidean discrete gravity in 3 dimensions.

### Discrete gravity on random tensor network and holographic Rényi entropy

- Computer Science
- 2017

The boundary many-body quantum state |Ψ〉 is constructed using random tensor networks as the holographic mapping, applied to the Wheeler-deWitt wave function of bulk Euclidean discrete gravity in 3 dimensions.

### Surface/State Correspondence as a Generalized Holography

- Physics
- 2015

We propose a new duality relation between codimension two space-like surfaces in gravitational theories and quantum states in dual Hilbert spaces. This surface/state correspondence largely…

### Holographic unitary renormalization group for correlated electrons - II: Insights on fermionic criticality

- PhysicsNuclear Physics B
- 2020

### Entanglement and complexity of purification in ( 1+1 )-dimensional free conformal field theories

- PhysicsPhysical Review Research
- 2020

Finding pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace is necessarily a challenging task. Nevertheless, such purifications play the…

### Tensor Network Contractions

- PhysicsLecture Notes in Physics
- 2020

This lecture notes focuses on the contraction algorithms of TN as well as some of the applications to the simulations of quantum many-body systems, and revisits the TN approaches from the perspective of multi-linear algebra and quantum simulation.

### Quantum criticality on a chiral ladder: An SU(2) infinite density matrix renormalization group study

- PhysicsPhysical Review B
- 2019

In this paper we study the ground state properties of a ladder Hamiltonian with chiral $SU(2)$-invariant spin interactions, a possible first step towards the construction of truly two dimensional…

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