spin chain in nLab

Contents

Contents

Idea

(…)

Examples

• Heisenberg model

• Kitaev spin chain

• (…)

• solid state physics

• Bethe ansatz

• integrable system

• BMN limit

References

General

The original articles:

• Hans Bethe, Zur Theorie der Metalle, Z. Phys.71, 205 (1931) (doi:10.1007/BF01341708)

Review:

• Andreas Schadschneider, Götz S. Uhrig: Part II of: Strongly Correlated Systems in Solid State Physics, lecture notes (2004) [pdf, pdf]

• Ingmar Saberi, An introduction to spin systems for mathematicians [arXiv:1801.07270]

Relation to tensor networks:

• Mari Carmen Banuls, Michal P. Heller, Karl Jansen, Johannes Knaute, Viktor Svensson, From spin chains to real-time thermal field theory using tensor networks (arXiv:1912.08836)

Claim of supersymmetric spin chains carrying braid group representations (“anyons”):

• Indrajit Jana, Filippo Montorsi, Pramod Padmanabhan, Diego Trancanelli, Topological Quantum Computation on Supersymmetric Spin Chains [arXiv:2209.03822]

On topological phases (i.e. gapped ground states) of spin chains:

• Houssam Abdul-Rahman, Marius Lemm, Angelo Lucia, Bruno Nachtergaele, Amanda Young, A class of two-dimensional AKLT models with a gap, in: Analytic Trends in Mathematical Physics, Contemporary Mathematics 741, AMS (2020) [arXiv:1901.09297, doi:10.1090/conm/741/14917]

On simulation of quantum spin chains on quantum computers:

• M. Gluza, M. Kliesch, Jens Eisert, Leandro Aolita, Fidelity witnesses for fermionic quantum simulations, Phys. Rev. Lett. 120 190501 (2018) [arXiv:1703.03152, doi:10.1103/PhysRevLett.120.190501]

A holographic CMT model for spin chains:

• Naoto Yokoi, Yasuyuki Oikawa, Eiji Saitoh, Holographic Dual of Quantum Spin Chain as Chern-Simons-Scalar Theory [arXiv:2310.01890&rbrack:

For single trace operators in super Yang-Mills theory

Identifiication of spin chain dynamics in the action of the dilatation operator in super Yang-Mills theory, specifically D=4 N=4 super Yang-Mills theory, on single trace operators/BMN operators and correspondence to Green-Schwarz superstrings on AdS5 under the AdS-CFT correspondence:

• J. A. Minahan, Konstantin Zarembo, The Bethe-Ansatz for N=4N=4 Super Yang-Mills, JHEP 0303 (2003) 013 (arXiv:hep-th/0212208)

• Niklas Beisert, Matthias Staudacher, The 𝒩=4\mathcal{N}=4 SYM Integrable Super Spin Chain,

  Nucl. Phys. B670:439-463, 2003 (arXiv:hep-th/0307042)

• Niklas Beisert, Sergey Frolov, Matthias Staudacher, Arkady Tseytlin, Precision Spectroscopy of AdS/CFT, JHEP 0310:037, 2003 (arXiv:hep-th/0308117)

Review includes

• A. V. Belitsky, Volker Braun, A. S. Gorsky, G. P. Korchemsky, Integrability in QCD and beyond, Int. J. Mod. Phys. A19:4715-4788, 2004 (arXiv:hep-th/0407232)

• Niklas Beisert, Luis Alday, Radu Roiban, Sakura Schafer-Nameki, Matthias Staudacher, Alessandro Torrielli, Arkady Tseytlin, et. al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99, 3 (2012) (arXiv:1012.3982)

For D3-D7 brane bound states and D3-D5 brane bound states:

• Marius de Leeuw, Tamás Gombor, Charlotte Kristjansen, Georgios Linardopoulos, Balázs Pozsgay, Spin Chain Overlaps and the Twisted Yangian (arXiv:1912.09338)

See also:

• Taro Kimura, Rui-Dong Zhu, Bethe/Gauge Correspondence for SOSO/SpSp Gauge Theories and Open Spin Chains, JHEP 2021 227 (2021) [arXiv:2012.14197, doi:10.1007/JHEP03(2021)227]

• Ziwei Wang, Rui-Dong Zhu, Bethe/Gauge Correspondence for A NA_N Spin Chains with Integrable Boundaries [arXiv:2401.00764]

Analogous spin chain aspects claimed to appear in D=6 N=(2,0) SCFT:

• Florent Baume, Jonathan J. Heckman, Craig Lawrie, 6D SCFTs, 4D SCFTs, Conformal Matter, and Spin Chains, Nuclear Physics B 967 (2021) 115401 [doi:10.1016/j.nuclphysb.2021.115401, arXiv:2007.07262]

• Jonathan J. Heckman, Qubit construction in 6D SCFTs, Physics Letters B 811 (2020) 135891 [doi:10.1016/j.physletb.2020.135891, arXiv:2007.08545]