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 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]

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]

Review:

• 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]

• Wikipedia, Quantum spin liquid