Fig. 1

Main panel: Schematic phase diagram in the temperature T—strain ε _xx space (with ε _yy  ≡ −ε _xx  > 0) under fixed interaction. Insets: The phase diagram in the interaction parameter (U−V) space for ε _xx  = ε _L (left inset) and ε _xx  = 0 (right inset). Here, ε _L (arrow) is the strain level for Lifshitz reconstruction. The ordering temperature of the various phases in the insets is higher where the background color is brighter. The white solid lines denote qualitatively the phase boundaries, and the red squares denote the two typical sets of interactions discussed in more detail in the text