  The electronic properties of graphene can be manipulated via mechanical
deformations, which opens prospects for studying the Dirac fermions in new
regimes and for new device applications. Certain natural configurations of
strain generate large nearly uniform pseudo-magnetic fields, which have
opposite signs in the two valleys, and give rise to flat spin- and
valley-degenerate pseudo Landau levels (PLLs). Here we consider the effect of
the Coulomb interactions in strained graphene with uniform pseudo-magnetic
field. We show that the spin/valley degeneracies of the PLLs get lifted by the
interactions, giving rise to topological insulator-like states. In particular,
when a nonzero PLL is quarter- or three-quarter filled, an anomalous quantum
Hall state spontaneously breaking time-reversal symmetry emerges. At
half-filled PLL, weak spin-orbital interaction stabilizes
time-reversal-symmetric quantum spin-Hall state. These many-body states are
characterized by the quantized conductance and persist to a high temperature
scale set by the Coulomb interactions, which we estimate to be a few hundreds
Kelvin at moderate strain values. At fractional fillings, fractional quantum
Hall states breaking valley symmetry emerge. These results suggest a new route
to realizing robust topological insulator states in mesoscopic graphene.
