  In the semi-classical regime, quantum fluctuations embedded in a Riemannian
spacetime can be effectively recast as classical back reactions and manifest
themselves in the form of non-minimal couplings between matter and curvature.
In this work, we exhibit that this semi-classical description can also be
applied within the teleparallel formulation. In the teleparallel formulation,
quantum fluctuations generically lead to non-minimal torsion-matter couplings.
Due to the equivalence between the (classical) Einstein gravity in the
Riemannian description and that in teleparallel description, some effective
models which were constructed using Riemannian description can be reproduced
completely using the teleparallel description. Besides, when the effective
quantum correction term is proportional to the torsion scalar $T$, we obtain a
subclass of novel $f(T,B,\mathcal{T})$ gravity, where $B$ is a boundary term,
and $\mathcal{T}$ is the trace of the energy-momentum tensor. Next, we
investigate the cosmological properties in this $f(T,B,\mathcal{T})$ theory by
assuming that the matter Lagrangian is solely constructed by a dynamical scalar
field. We exhibit some interesting cosmological solutions, such as those with
decelerating expansion followed by a late-time accelerating phase. In addition,
the non-minimal torsion-matter couplings induced by quantum corrections
naturally lead to energy transfers between gravity and cosmological fluids in
the universe.
