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].
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 4 apr 2021