A theorem on extensive ground state entropy, spin liquidity and some related models

An exact mechanism is written down to guarantee extensive residual ground state entropy and spin liquidity in spin-1/2 lattice models with bond-dependent couplings. It is based on the presence of extensively large and mutually non-commuting (``\guillemotleft anticommuting\guillemotright'') sets of local conserved quantities with a gauge-like character. This mutual algebra is similar to those of spin-1/2 degrees of freedom however arising in the structure of local conserved charges whose support is not restricted to a single lattice site. The general theorem is first pedagogically illustrated through a variant of the familiar one-dimensional quantum Ising model featuring such an \guillemotleft anticommuting\guillemotright$~$structure. This leads to classical spin liquidity co-existing with quantum Ising order. The rest of the paper is then devoted to applications in higher dimensions with more general \guillemotleft anticommuting\guillemotright$~$structures which voids spin or magnetic ordering altogether. Proofs of the resultant quantum spin liquidity are given through an analysis of static and dynamic $n$-point spin correlators relying solely on the \guillemotleft anticommuting\guillemotright$~$algebraic structure of the constructed models. It is not evident if they admit exact solutions using known techniques. The precise nature of these quantum spin liquids is thus an open question including the existence of a quasiparticle description for these models. We compare and contrast them with other well-known quantum spin liquids.