  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.
