Poles-zeros duality in semi-holographic Mott insulators

Inspired by the poles-zeros duality of Green's functions that appears in transitions into Mott-insulating phases in strongly correlated condensed matter systems, we propose a semi-holographic approach to Mott insulators. In this model, a fundamental fermion is coupled to a large-$N$, strongly interacting sector that generates a self-energy for the fundamental fermion's Green's function. This coupling amounts to a hybridization of the fundamental fermion with a strongly correlated fermionic composite. Within the holographic framework, at large $N$, the Green's function of the composite fermion naturally exhibits a poles-zeros duality. Zeros of the Green's function are caused by the poles of the self-energy that correspond to collective many-body excitations of the holographic strongly interacting sector. We calculate the spectral function of the fundamental fermion, from which we characterize the semi-holographic metallic and the Mott-insulating phases. In addition to the new physical interpretation of the zeros, our analysis yields a well-defined picture of the poles-zeros duality in terms of the freedom to choose between standard and alternative quantization in the strongly coupled sector.