A quantum spin liquid (QSL) is a magnetic state of matter in which electron spins interact strongly but avoid freezing into the static, symmetry-breaking order (ferromagnetism, antiferromagnetism, and so on) that most magnetic materials eventually adopt as they cool. This typically arises from geometric frustration — a lattice geometry, such as the triangular or kagome lattice, on which antiferromagnetic interactions cannot simultaneously satisfy every pair of neighboring spins — which keeps the spins fluctuating and entangled down to zero temperature rather than letting them lock into a classical pattern.
The theoretical language for QSLs is usually a parton (or slave-particle) construction: the physical electron operator is formally split into a fractionalized spin-carrying fermion (spinon) and a charge-carrying boson (chargon) ,
subject to a constraint (typically single occupancy per site) that keeps the split from over-counting states. The spinon is coupled to an emergent gauge field that has no counterpart in the original microscopic Hamiltonian. Which parton construction correctly describes a given candidate material is constrained by its projective symmetry group, the pattern of how the lattice’s physical symmetries act projectively on the fractionalized spinons. Several real triangular-lattice insulators are considered candidate QSLs on the basis of NMR, neutron-scattering, and thermal-transport measurements showing no magnetic ordering down to the lowest accessible temperatures, and some of these materials are separately observed to become superconducting under applied pressure or chemical doping — connecting the fractionalized QSL phase to the more familiar physics of unconventional superconductivity. When the chargon condenses (), spinon and chargon recombine into a conventional (non-fractionalized) electron — the mechanism by which a QSL confines into an ordinary ordered phase.
Related papers
- Anderson, “Resonating valence bonds: A new kind of insulator?”, Materials Research Bulletin 8, 153 (1973) — the original proposal that frustrated magnets could host a liquid-like, non-ordered ground state.
- Wen, “Quantum orders and symmetric spin liquids”, Phys. Rev. B 65, 165113 (2002) — introduces the projective-symmetry-group classification of parton mean-field states used to organize candidate spin-liquid phases.