Tensor Networks

In General
* Idea: A collection of tensors with indices connected according to a network pattern, used to efficiently represent quantum many-body states of matter based on their local entanglement structure; A tool used to approximate ground states of local Hamiltonians on a lattice; Their data compression can dramatically reduce the growth of computational complexity with the scale of the system, and their diagrammatic language provides a useful visual intuition.
* MERA: Multiscale entanglement renormalization ansatz.
@ Books, intros: Orús AP(14)-a1306; Montangero 17; Biamonte & Bergholm CP-a1708; Baker et al CJP-a1911; Biamonte a1912-ln.
@ General references: Sachdev Phy(09); Bridgeman & Chubb JPA(17)-a1603-ln [with problems]; Nezami & Walter a1608 [multipartite entanglement structure]; Wille et al PRB(17)-a1609; Al-Assam et al JSM-a1610 [software library]; Robeva & Seigal a1710 [on hypergraphs]; Fishman et al PRB(18)-a1711 [contracting]; Bhattacharyya et al a1805 [Lorentzian, and causal structures]; Glasser et al a1806 [probabilistic graphical models]; Christandl et al SciPost(20)-a1809 [tensor network representations]; Roberts et al a1905 [TensorNetwork open source library].
@ Renormalization: Dittrich et al NJP(16)-a1409 [decorated]; Evenbly & Vidal PRL(15)-a1412; Sasakura & Sato PTEP(15)-a1501 [for random tensor networks]; Hauru et al PRB(18)-a1709 [using graph-independent local truncations]; > s.a. renormalization group.
@ Other techniques: Biamonte et al AIP(11)-a1012 [factorization]; Ran et al a1708-ln [contractions]; Schmoll et al PRL(20)-a1911 [lattices of high connectivity].
> Online references: see John Baez page; Perimeter Institute tensor networks initiative page.
> Related topics: see quantum phase transitions.

Specific Types of Systems
* Gauge theories: Tensor Network numerical simulations are free of the sign problem affecting Monte Carlo ones.
@ Quantum mechanics: Bauer a2003 [systematic approach, information-theoretic perspective].
@ Quantum many-body systems: Wahl PhD(15)-a1509; Schrodi et al PRB(17)-a1703; Silvi et al a1710; Ran et al 20 [contractions].
@ Gauge theories: Tagliacozzo et al PRX(14)-a1405 [lattice]; Buyens et al PoS-a1511; Silvi et al Quant(17)-a1606 [finite-density phase diagram]; Bañuls et al EPJwc(17)-a1611 [lattice, overcoming the Monte Carlo sign problem]; Magnifico et al a2011 [at finite density].
@ And gravity: Chen et al PRD(16)-a1601 [emergent geometries]; Han & Hung PRD(17)-a1610 [and lqg]; May JHEP(17)-a1611, a1709-MSc [for dynamic spacetimes]; Chirco et al CQG(18)-a1701, PRD(18)-a1711 [and group field theory, Ryu-Takayanagi formula]; Han & Huang JHEP(17)-a1705 [discrete gravity and Regge calculus]; Dong & Zhou a1804 [entanglement, spacetime as generative network of quantum states, and Susskind's QM = GR]; Asaduzzaman et al a1905 [2D]; Guo JPA(20)-a1906 [quantum causal histories]; Colafranceschi & Oriti a2012 [and group field theory states]; > s.a. Mike Zaletel talk.
@ Other specific types of systems: Alsina & Latorre a1312 [frustrated anti-ferromagnetic systems]; Orús AP(14) [introduction]; Orús EPJB(14)-a1407 [for strongly correlated systems]; Bao et al PRD(17)-a1709 [de Sitter spacetime and MERA]; > s.a. renormalization; Transport Phenomena.
@ And holography: Orús EPJB(14)-a1407 [fermionic TNs, entanglement, MERA]; Ouellette Quanta(15); Bao et al PRD(15)-a1504 + Carroll blog(15)may [AdS/MERA correspondence, consistency conditions]; Bhattacharyya et al JHEP(16)-a1606 [perturbations and Coxeter construction]; Czech et al JHEP(17)-a1612 [with defects].
@ Variants: Rader & Läuchli PRX(18) [iPEPS, infinite projected entangled pair states]; Tilloy & Cirac PRX(19)-a1808 + Pervishko & Biamonte Phy(19) [continuous, for quantum fields].

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