Properties of the spin-liquid phase in the vicinity of the Lifshitz transition from Neel to spin-spiral state in frustrated magnets

Three decades ago, Ioffe and Larkin pointed out a generic mechanism for the formation of a gapped spin liquid. In the case when a classical two-dimensional (2D) frustrated Heisenberg magnet undergoes a Lifshitz transition between a collinear Ned phase and a spin-spiral phase, quantum effects usually lead to the development of a spin-liquid phase sandwiched between the Ned and spin-spiral phases. In this work, using field theory techniques, we study properties of this universal spin-liquid phase. We examine the phase diagram near the Lifshitz point and calculate the positions of critical points, excitation spectra, and spin-spin correlation functions. We argue that the spin liquid in the vicinity of 2D Lifshitz point (LP) is similar to the gapped Haldane phase in integer-spin one-dimensional chains. We also consider a specific example of a frustrated system with the spiral-Ned LP, the J(1)-J(3) antiferromagnet on the square lattice that manifests the spin-liquid behavior. We present numerical series expansion calculations for this model and compare results of the calculations with predictions of the developed field theory.