  We explore emergent geometry of the spacetime at the microscopic scale by
adiabatic transport of a quasi-coherent state of a fermionic string, with
quantum spacetime described by the matrix theory (BFSS matrix model). We show
that the generator of the Berry phase is the shift vector of the spacetime
foliation by spacelike surfaces associated with the quasi-coherent state. The
operator-valued generator of the geometric phase of weak adiabatic transport is
the Lorentz connection of the emergent geometry which is not torsion free at
the microscopic scale. The effects of the torsion seem consistent with the
usual interpretation of the Berry curvature as a pseudo magnetic field.
