  Unconventional symmetry breaking without spin order,such as the rotational
symmetry breaking (=nematic or smectic) orders as well as the spontaneous
loop-current orders, have been recently reported in cuprate superconductors and
their related materials.They are theoretically represented by non-$A_{1g}$
symmetry breaking in self-energy, which we call the form factor $f_{k,q}$.In
this paper, we analyze typical Hubbard models by applying the
renormalization-group (RG) method, and find that various unconventional
ordering emerges due to the quantum interference among spin fluctuations. Due
to this mechanism,nematic ($q=0$) and smectic ($q \ne 0$)bond orders with
$d$-wave form factor appear $f_{k,q}\propto \cos k_x - \cos k_y$ in both
cuprates and $\kappa$-(BEDT-TTF)$_2$X. The derived bond orders naturally
explain the pseudogap behaviors in these compounds. The quantum interference
also induces various current orders with odd-parity form factor. For example,
we find the emergence of the charge and spin loop-current orders with $p$-wave
form factor in geometrically frustrated Hubbard models. Thus, rich quantum
phase transitions with $d$- and $p$-wave form factors are driven by the
paramagnon interference in many low-dimensional Hubbard models.
