According to the celebrated Onsagar-Lifshitz paradigm, the observation of Shubnikov de-Haas and de-Haas van Alphen (SdHvA) oscillations is an indication of the presence of `closed orbit Fermi surface in the bulk. We present a real-space based calculation of SdHvA oscillations in generalized quasi-one-dimensional lattices by relaxing the quasi-classical approximations embedded in this decades old Onsagar-Lifshitz paradigm. We find that sizable quantum oscillation can arise from `open Fermi surfaces as long as cyclotron orbits can form in real-space with finite, but not necessarily equal, electron hopping along both x- and y-directions. Our results quantitatively explain the puzzling emergence of SdHvA oscillation in various quasi-one-dimensional materials, including the chain state of YBa2Cu3O6 cuprates, organic materials, various ladder compounds, weakly coupled linear chains, or quantum wires, and other related systems.
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