  In the field of quantum magnetism, the advent of numerous spin-orbit assisted
Mott insulating compounds, such as the family of Kitaev materials, has led to a
growing interest in studying general spin models with non-diagonal interactions
that do not retain the SU(2) invariance of the underlying spin degrees of
freedom. However, the exchange frustration arising from these non-diagonal and
often bond-directional interactions for two- and three-dimensional lattice
geometries poses a serious challenge for numerical many-body simulation
techniques. In this paper, we present an extended formulation of the
pseudo-fermion functional renormalization group that is capable of capturing
the physics of frustrated quantum magnets with generic (diagonal and
off-diagonal) two-spin interaction terms. Based on a careful symmetry analysis
of the underlying flow equations, we reveal that the computational complexity
grows only moderately, as compared to models with only diagonal interaction
terms. We apply the formalism to a kagome antiferromagnet which is augmented by
general in-plane and out-of-plane Dzyaloshinskii-Moriya (DM) interactions, as
argued to be present in the spin liquid candidate material herbertsmithite. We
calculate the complete ground state phase diagram in the strength of in-plane
and out-of-plane DM couplings, and discuss the extended stability of the spin
liquid of the unperturbed kagome antiferromagnet in the presence of these
couplings.
