  In noncentrosymmetric crystals with broken inversion symmetry $\mathcal{I}$,
the $I-V$ ($I$: current, $V$: voltage) characteristic is generally expected to
depend on the direction of $I$, which is known as nonreciprocal response and,
for example, found in p-n junction. However, it is a highly nontrivial issue in
translationally invariant systems since the time-reversal symmetry
($\mathcal{T}$) plays an essential role, where the two states at crystal
momenta $k$ and $-k$ are connected in the band structure. Therefore, it has
been considered that the external magnetic field ($B$) or the magnetic order
which breaks the $\mathcal{T}$-symmetry is necessary to realize the
nonreciprocal $I-V$ characteristics, i.e., magnetochiral anisotropy. Here we
theoretically show that the electron correlation in $\mathcal{I}$-broken
multi-band systems can induce nonreciprocal $I-V$ characteristics {\it without}
$\mathcal{T}$-breaking. An analog of Onsager's relation shows that
nonreciprocal current response without $\mathcal{T}$-breaking generally
requires two effects: dissipation and interactions. By using nonequilibrium
Green's functions, we derive general formula of the nonreciprocal response for
two-band systems with onsite interaction. The formula is applied to Rice-Mele
model, a representative 1D model with inversion breaking, and some candidate
materials are discussed. This finding offers a coherent understanding of the
origin of nonreciprocal $I-V$ characteristics, and will pave a way to design
it.
