Degeneracies and exotic phases in an isotropic frustrated spin-1/2 chain

In the presence of an axial magnetic field, a frustrated isotropic J1-J2 model system shows many exotic phases, such as vector chiral and multipolar phases. In this paper, the phase boundaries of these exotic phases are calculated based on the order parameters, energy level crossings and magnetization jumps in the system. The order parameter of the vector chiral phase is calculated using the broken symmetry states at a finite magnetic field. The exact diagonalization and the density matrix renormalization group results are used to show that the vector chiral phase exists only in a narrow range of J2/J1 parameter space. In the quadrupolar phase, the magnetization jumps can be associated with the binding energy of two magnons localized at two different legs of the zigzag chain. The energy level crossings and degeneracies in the presence of the axial magnetic field are studied in detail using the exact diagonalization method.