# Entanglement Renormalization In Two Spatial Dimensions

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### The density-matrix renormalization group - Journals Royal

by U Schollwöck 2011 Cited by 38 the alternative view of the DMRG as a variational method in the space of 2. Density-matrix renormalization group in one dimension. (a) Matrix product states low-entanglement approximation to a quantum state becomes most obvious.

### Evidence of quantum phase transition in real-space - Nature

by SS Kumar 2017 Cited by 5 In this work, we show that the area law is violated in two spatial dimensional model and analytically using quantum Information tools like entanglement spectra, role in the renormalization of the Feynman propagators in the high energy

### ENTANGLEMENT ENTROPY OF TWO DIMENSIONAL QUASI

by AB Weiss 2015 ticular vector bundle over the (d + 1)-dimensional RG mapping space, called a jet 10.1.1 Exact RG equations: Wilson-Polchinski renormalization in two steps

### Strong disorder RG approach - European Physical Journal

by F Iglói 2018 Cited by 41 11.1 Real-space renormalization for random walks in random media different dimensions d in Section 2, the effects of long- ranged interactions in entanglement entropy SL of a finite block of size L in an infinite system is

### Entanglement Renormalization in two spatial dimensions:

in two spatial dimensions: MERA = multi-scale entanglement renormalization ansatz Entanglement renormalization coarse-graining transformation: L. Ψ.

### Entanglement Renormalization in Two Spatial Dimensions

by G Evenbly 2009 Cited by 158 We propose and test a scheme for entanglement renormalization capable of addressing large two- dimensional quantum lattice systems. In a translationally

### Master's thesis: Multiscale Entanglement Renormalisation

by M Hauru 2013 Cited by 8 multiscale entanglement renormalisation ansatz MERA tensor network MERA and MERA in two spatial dimensions. much more in-depth and extensive Scaling and Renormalization in Statistical Physics by Cardy [7].

### Entanglement renormalization and two dimensional string theory

by J Molina-Vilaplana 2016 Cited by 13 〉 corresponds to a point on a two dimensional hyperbolic space. It may be argued that once provided a suitable measure of the dis- tance

### Studying dynamics in two-dimensional quantum lattices using

by B Kloss 2020 Cited by 2 systems), this does not hold in two spatial dimensions [5 7]. entanglement renormalization ansatz tensor networks for quantum critical

### Scale-Invariant Continuous Entanglement Renormalization of

by SK Chu 2019 Cited by 1 entanglement renormalization for a two-band Chern insu- lator model. fermion field ψ(x) in d spatial dimensions, we pick L = −(i=2). R.

### Entanglement Entropy and Variational Methods: Interacting

by JS Cotler 2016 Cited by 9 We find that in 1+1 and 2+1 dimensions, the entanglement entropy of φ4 It is important to distinguish the state space of the quantum field theory where the crete meaning through the regularization and renormalization

### Real-space Renormalization Group Methods in the Age of

by M Bal 2018 Cited by 1 Secondly, we rephrase tensor network renormalization for two-dimensional classical 3.4.2 Entanglement structure of MERA: correlations in scale space 84.

### 20w5064: Fractons and Beyond - Banff International Research

by X Chen Wilbur Shirley talked about entanglement renormalization of gapped fracton models. Gapped fractonic terize topological orders in two spatial dimensions.

### Simulation of interacting fermions with entanglement

by P Corboz 2009 Cited by 118 teracting fermions, such as the Hubbard model, remain highly controversial in two spatial dimensions. Recently, entanglement renormalization [3] has been.

### univERsity oF copEnhAGEn

by IH Kima Cited by 24 Entanglement renormalization, quantum error correction, and bulk causality This implies that two operators that are largely separated in scales critical behavior of one-dimensional quantum many-body systems. noted that the isometry Ws maps vectors of the Hilbert space at scale s to the Hilbert.

### Entanglement Renormalization, Quantum Error - QuTech

by IH Kim 2017 Cited by 24 Space and Time Entanglement Renormalization, Quantum Error Correction, and Bulk 2. Correctability condition formulated. 3. Positive scaling dimension

### Rigorous Free-Fermion Entanglement Renormalization from

by J Haegeman 2018 Cited by 20 surface in the two-dimensional model requires a special kind of circuit architecture and its real-space entanglement renormalization structure.

### Low entanglement wavefunctions

by GKL Chan Cited by 27 forms the variational space of the density matrix renormalization group algo- rithm. Because of In two-dimensional system, the boundary area can scale as the

### Studying dynamics in two-dimensional quantum - SciPost

by B Kloss Cited by 2 systems), this does not hold in two spatial dimensions [5 7]. entanglement renormalization ansatz tensor networks for quantum critical

### Multi-scale entanglement renormalization ansatz - Centro de

24 Jul 2015 Variational class of states for 1d systems, which extends in space and scale. Variational parameters for different length scales stored in

### Topological Entanglement Entropy of Black Hole Interiors

by E Howard 2020 Cited by 9 theory on (d 2)-dimensional AdSd2 space, living on the boundary. tools from many-body physics like entanglement renormalization and

### Corner space renormalization method for driven-dissipative

by S Finazzi 2015 Cited by 77 to two spatial dimensions is challenging and currently un- der intense tions and quantum entanglement between systems A and. B while

### arXiv:1810.12838v2 [hep-lat] 6 Nov 2018 - PUBDB

by MC Bañuls 2018 Cited by 16 The spatial dimensions and sizes of the systems amenable to TNS studies are still far The entanglement between two halves of the chain is upper- [10] B. Swingle, Entanglement renormalization and holography, Phys.

### Problem Set - Perimeter Institute

where each index i takes two values i = 0,1, vl and vr and χ-dimensional vectors, and A0 a basis of the Hilbert space of one lattice site (in our example, i = 0,1) and two The multi-scale entanglement renormalization ansatz (MERA) (see Fig.

### Tensor networks and the renormalization group - UWSpace

by M Hauru 2018 for implementation of real-space renormalization in higher dimensions, and discuss some of χ = 2 MPS states have entanglement only between near-by sites.

### Entanglement renormalization in two spatial dimensions

by G Evenbly 2008 Cited by 158 Entanglement renormalization in two spatial dimensions. G. Evenbly1 proposed as a real-space renormalization group (RG) method [2] to

### Holographic Branching and Entanglement Renormalization

by G Evenbly It produces the multi-scale entanglement renormalization ansatz (MERA) [2], a tensor network state one and two spatial dimensions [3, 4]. In 1D, the MERA is

### Entanglement and Tensor Network States - cond-mat.de

by J Eisert Cited by 112 1 Correlations and entanglement in quantum many-body systems. 2. 1.1 Quantum 3.2 Multi-scaleentanglementrenormalization 32 Clearly, the dimension of the Hilbert space grows exponentially with the system size,

### Entanglement renormalization and holography - [email protected]

by B Swingle 2012 Cited by 758 holographic dimension. This picture connects two new tools in many-body physics: entanglement renormalization and holographic gauge/ take to have linear size L in d spatial dimensions. Locality suggests that the

### Real Space Renormalization in Statistical Mechanics - James

by E Efrati Cited by 87 Real Space Renormalization in Statistical Mechanics. Efi Efrati,1, ∗ Zhe These calculations describe three models for two-dimensional sys- tems: The Ising [46] Guifre Vidal Entanglement Renormalization: an intro- duction chapter of the

### Multiscale Entanglement Renormalization Ansatz in Two

by L Cincio 2008 Cited by 94 We propose a symmetric version of the multiscale entanglement renormalization ansatz in two spatial dimensions (2D) and use this ansatz to

### Topological Entanglement Entropy of Black Hole Interiors

by E Howard Cited by 9 theory on (d ю 2)-dimensional AdSdю2 space, living on the boundary. holography and entanglement renormalization led to a full holographic picture of the.

### Multi-partite entanglement - ResearchGate

by M Walter 2016 Cited by 55 1 Introduction. 1. 2 General theory. 2. 2.1 Classifying pure state entanglement is associated with a finite-dimensional Hilbert space Hi ≃ Cdi , for some di < ∞. tioning of the various variants of the density matrix renormalization group

### Combining Variational Optimization with Entanglement

On the other hand, the Multiscale Entanglement Renormalization. Ansatz (MERA), is able ods is based on the fact that the Hilbert space containing the states of by multiplying the dimensions of all legs connected to both tensors, counting

### Classical simulation of quantum many-body systems by

by Y Huang 2015 Cited by 15 density matrix renormalization group is the leading numerical method for Quantum many-body systems in two and higher dimensions (2+D) can host a local Hamiltonians in any spatial dimension satisfy an area law for entanglement, but a

### The Multiple Entanglement Renormalization Ansatz and the

by JC Borger From a critical state it creates an extra spatial dimension resembling a spatial AdS slice. In this thesis this resemblance is further studied. Then two tensor

### Lessons for gravity from entanglement - Centre for High

for the dual space-time [17]. This was used [9] S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP. 0608 (2006) Holographic Geometry of Entanglement Renormalization in Quantum Field Theo- ries, JHEP

### De Sitter Space as a Tensor Network - Caltech Authors

by N Bao 2017 Cited by 51 tiscale Entanglement Renormalization Ansatz) tensor network, and ask what can the two-dimensional geometry of the graph is mapped to the

### JHEP07(2020)149 - Inspire HEP

by JJ Fernández-Melgarejoa Cited by 6 The multiscale entanglement renormalization ansatz (MERA) [1, 2], correlations between small adjacent regions of space at each length

### Momentum-space entanglement after a quench in one

by R Lundgren 2019 Cited by 3 We numerically investigate the momentum-space entanglement entropy and entanglement spectrum of the random-dimer model renormalization group algorithms [46, 47]. For the two-dimensional disordered system, the real-space EE.

### Tensor Network Methods for Quantum Phases - The University

by J Bridgeman 2017 Chapter 4: Anomalies and entanglement renormalization. This chapter In one (spatial) dimension, this model exhibits a quantum phase transition at J simplest model realising such a phase is the two-dimensional toric code [2]. This model

### Entanglement Renormalization and Black Holes - Kavli IPMU

In quantum mechanics, a physical state is described by a vector in. Hilbert space. If we consider a spin of an electron (= two dimensional Hilbert space), a state is

### Causal structure of the entanglement renormalization ansatz

by C Bény 2013 Cited by 86 2. The multiscale entanglement renormalization ansatz (MERA), introduced in the coarse-graining is such that the Hilbert space dimension

### Anomalies, Entanglement and Boundary Geometry in

by KW Huang 2018 and a three-dimensional boundary electron is found to have two boundary central As fixed points of renormalization group flow, conformal field theories play a space-time dimension, the connection between entanglement entropy and

### MACHINE LEARNING BY TWO-DIMENSIONAL HIER

by D Liu 2018 Cited by 31 derived from the multipartite entanglement renormalization ansatz (MERA). This tion that satisfies ΨΨ† = I; it compresses a dN -dimensional space to

### Real-space renormalization yields finitely correlated states: EPAPS

(MERA) states for D > 1 spatial dimensions to projected entangled pair states (PEPS), it is tensor network states [1, 2] for which the entanglement en-.

### Holographic Spacetimes From Entanglement Renormalization

Example: Fermi surface. Entanglement entropy, shape dependence. Renyi entropy. Finite T generalization. Multiple regions, non-convex regions.

### A polynomial-time algorithm for the ground state of 1D gapped

by Z Landau 2015 Cited by 112 fraction of this exponential space, and the resulting manifold has been called the implies that the associated quantum state has small entanglement rank. MPS representations, the density matrix renormalization group12. (DMRG), which in two dimensions15 or systems out of equilibrium16, but many.

### Momentum-space Entanglement and Renormalization in

by V Balasubramanian Cited by 119 Momentum-space Entanglement and Renormalization in Quantum Field. Theory. Physical field theories with n potentials in various dimensions. The scale example, the Hilbert space for two identical oscillators could be

### Entanglement Renormalization and Two Dimensional String

cMERA (Haegeman et al 2011) is a real-space RG in a hamiltonian framework at the level of wavefunctions. cMERA represents the wavefunction of the system