Classical SL: =spin ice, e.g. in Dy2Ti2O7, large spin, frustration, but eventually order at ~0.5K
QSL: VBS(valence bond solid) is not QSL (b/c breaks translation, and more importantly, not long-range entangled) and have been found in many materials; RVB(resonating valence bond) is QSL(Anderson predict it to be physics of High Tc SC in 1987)
Understanding of existence of different QSLs: low energy excitation due to long-range VB configuration, also possible in short-range RVB by simply rearranging configurations. (And hence this is the motivation for classification of QSL, e.g. PSG.)
Defining property of QSL: long range entanglement; fractional excitation(spinon)(they can be shown to be equivalent); no symmetry breaking. Fractional excitations also occur in spin ice, but not true coherent quasiparticles.
long range entanglement = fractional (spinon) excitation = deconfined phase = boundary tensionless (spinons can space very long while only causing finite amount of energy). Spin ice becomes confined before 0 K, but QSL remains deconfined at 0 K.
Spinons are well established in one-dimensional (1D) systems, in which they occur as domain walls(Fig. 4a). A spinon can thus be created similarly to a monopole in spin ice, by flipping a semi-infinite string of spins. A key difference, however, is that in one dimension the only boundary of such a string is its end point, so the string is guaranteed to cost only a finite energy from this boundary. By contrast, in two or three dimensions, the boundary of a string extends along its full length. A string would naturally be expected to have a tension (that is, there is an energy cost proportional to its length). String tension represents confinement of the exotic particle, as occurs for quarks in quantum chromodynamics. This is avoided in spin ice by the special form of the nearest-neighbour Hamiltonian. However, when spin ice is in equilibrium, corrections to this form would be expected to lead to monopole confinement at low temperatures. In a true 2D or 3D QSL, the string associated with a spinon remains robustly tensionless even at T = 0 K, owing to strong quantum fluctuations (Fig. 4c). This can be understood from the quantum superposition principle: rearranging the spins along the string simply reshuffles the various spin or valence-bond configurations that are already superposed in the ground state. Detailed studies of QSL states have shown that higher-dimensional spinons can have varied character. They may obey Fermi–Dirac36, Bose–Einstein37 or even anyonic statistics (see page 187). They may be gapped (that is, require a non-zero energy to excite) or gapless, or they may even be so strongly interacting that there are no sharp excitations of any kind38..
Experimental technique: nuclear magnetic resonance (NMR) and muon spin resonance experiments prove magnetic moments; specific heat (compare with theory); thermal transport and elastic/inelastic neutron scattering (excitation properties).
Materials are distinguished by their degree of Mott insulator (U/t).