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 symmetry breaking in the correlated hopping integrals, 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 orderings emerge due to the quantum interference among spin fluctuations. Due to this mechanism, nematic (q = 0) and smectic (q ≠ 0) bond orders with d-wave form factor f_k,q ∝ cosk_x − cok_y appear in both cuprates and κ-(BEDT-TTF)₂X. The derived bond orders naturally explain the pseudogap behaviors in these compounds. The quantum interference also induces various current orderings 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.

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