Phase diagram of a frustrated two-dimensional J 1-J 2-J 3 quantum antiferromagnet: An approach based on spherically symmetric green’s functions

Abstract

The phase diagram of the frustrated J 1-J 2-J 3 S = 1/2 Heisenberg model on a square lattice is studied in the range of parameters corresponding to the spin-liquid state of the system. The study is performed using the self-consistent two-time retarded spin-spin Green’s functions, which do not break both translational and SU(2) symmetries. The inclusion of the damping of spin fluctuations allows us to obtain a good agreement with the cluster calculations. Using a consistent analytical approach, we have found continuous transitions via the spin-liquid state between the phases with three types of the long-range order: checkerboard, stripe, and (k, k) helical. In addition, there are indications confirming the existence of the (k, π) helical phase.