Spinons in a Crossed-Chains Model of a 2D Spin Liquid

Using the random phase approximation, we show that a crossed-chains model of spin- $1/2$ Heisenberg chains with frustrated interchain couplings has a nondimerized spin-liquid ground state in 2D, with deconfined spinons as the elementary excitations. The results are confirmed by a bosonization study, which shows that the system is an example of a “sliding Luttinger liquid.” In an external field, the system develops an incommensurate field-induced long-range order with a finite transition temperature.