nLab quantum spin liquid

Idea

A topological state of matter governed by a kind of $\mathbb{Z}/2$-gauge theory and thought to exhibit topological order.

Related concepts

• topological phase of matter

• topological order

References

The state was originally conceived under the name resonating valence bond states in:

• Philip W. Anderson, Resonating valence bonds: A new kind of insulator?, Materials Research Bulletin

  8 2 (1973) 153-160 [doi:10.1016/0025-5408(73)90167-0]

Further early discussion:

• Nicholas Read, B. Chakraborty, Statistics of the excitations of the resonating-valence-bond state, Phys. Rev. B 40 (1989) 7133 [doi:10.1103/PhysRevB.40.7133]

Textbook account:

• Xiao-Gang Wen: Mean-field theory of spin liquids and quantum order, chapter 9 in: Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons, Oxford Academic (2007) [doi:10.1093/acprof:oso/9780199227259.001.0001, pdf]

Further review:

• Lucile Savary, Leon Balents, Quantum Spin Liquids, Rep. Prog. Phys. 80 016502 (2017) [arXiv:1601.03742, doi:10.1088/0034-4885/80/1/016502]

• C. Broholm et al.: Quantum spin liquids, Science 367 6475 (2020) [doi:10.1126/science.aay0668]

• Steven A. Kivelson, Shivaji Sondhi, 50 years of quantum spin liquids, Nature Reviews Physics, May 26, 2023 [arXiv:2305.18103, doi:10.1038/s42254-023-00596-x]

• Subir Sachdev: Lectures on insulating and conducting quantum spin liquids [arXiv:2512.23962]

See also:

• Wikipedia, Quantum spin liquid

As examples of Kitaev materials:

• Simon Trebst, Kitaev Materials, [arXiv:1701.07056]

• David Mandrus, New Kitaev Materials (Oct 2019) [pdf]

• Simon Trebst, Ciarán Hickey: Kitaev Materials, Physics Reports 950 (2022) 1-37 [doi:10.1016/j.physrep.2021.11.003]

• Kitaev Materials, npj Quantum Materials collection (2024)

Understanding as topological order with anyon-excitations:

• V. Kalmeyer, Robert B. Laughlin, Equivalence of the resonating-valence-bond and fractional quantum Hall states, Phys. Rev. Lett. 59 (1987) 2095 [doi:10.1103/PhysRevLett.59.2095]

• Xiao-Gang Wen, Frank Wilczek, Anthony Zee, Chiral spin states and superconductivity, Phys. Rev. B 39 (1989) 11413 [doi:10.1103/PhysRevB.39.11413]

• Andrew M. Essin, Michael Hermele, Classifying fractionalization: symmetry classification of gapped $\mathbb{Z}_2$ spin liquids in two dimensions, Phys. Rev. B 87 104406 (2013) [arXiv:1212.0593, doi:10.1103/PhysRevB.87.104406]

• Kyusung Hwang, Anyon condensation and confinement transition in a Kitaev spin liquid bilayer, Phys. Rev. B 109 134412 (2024) [arXiv:2301.05721, doi:10.1103/PhysRevB.109.134412]