Frustrated quantum two-dimensional J_1-J_2-J_3 antiferromagnet in a spherically symmetric self-consistent approach

摘要

In the framework of a spherically symmetric self-consistent approach to two-time retarded spin-spin Green's functions, we develop the theory of a two-dimensional frustrated J_1-J_2-J_3 quantum S=1/2 antiferromagnet. We show that taking the damping of spin fluctuations into account is decisive in forming both the spin-liquid state and the state with long-range order. In particular, the existence of damping allows explaining the scaling behavior of the susceptibility χ(q, ω) of the CuO_2 cuprate plane, the behavior of the spin spectrum in the two-plane case, and the occurrence of an incommensurable χ(q, ω) peak. In the case of the complete J_1-J_2-J_3 model, in a single analytic approach, we find continuous transitions between three phases with long-range order ("checkerboard," stripe, and helical (q, q) phases) through the spin-liquid state. We obtain good agreement with cluster computations for the J_1-J_2-J_3 model and agreement with the neutron scattering data for the J_1-J_2 model of cuprates.