  Efficiently bounding large determinants is an essential step in
non-relativistic fermionic constructive quantum field theory to prove the
absolute convergence of the perturbation expansion of correlation functions in
terms of powers of the strength $u\in \mathbb{R}$ of the interparticle
interaction. We provide, for large determinants of fermionic convariances,
sharp bounds which hold for all (bounded and unbounded, the latter not being
limited to semibounded) one-particle Hamiltonians. We find the smallest
universal determinant bound to be exactly $1$. In particular, the convergence
of perturbation series at $u=0$ of any fermionic quantum field theory is
ensured if the matrix entries, with respect to some fixed orthonormal basis, of
the covariance and the interparticle interaction decay sufficiently fast. Our
proofs use H\"older inequalities for general non-commutative $L^{p}$-spaces
derived by Araki and Masuda.
