Adiabatic transport of neural network quantum states

Variational quantum calculations have offered a controllable and powerful framework for capturing many-body quantum physics for decades. The recent introduction of expressive neural network quantum states has made it possible to accurately represent complex ground-state wavefunctions across the phase diagram for many Hamiltonians of interest. In this work, we introduce generalized variational representations of low-lying excited states, a key ingredient in the characterization of phases of matter and in the modeling of spectral properties. Exploiting continuity in Hamiltonian parameters, we adiabatically connect spectra of diagonalizable unperturbed Hamiltonians with fully interacting states at finite coupling, allowing us to tractably connect ground and excited states at different points of the phase diagram. Tests performed on spin Hamiltonians show an accurate representation of excited states and gaps closing at criticality. These results are achieved using a formalism of adiabatic gauge potentials (AGPs) which we use to derive a set of general update equations that can be seamlessly integrated with any variational calculation.