  Quantum phase transitions are a ubiquitous many-body phenomenon that occurs
in a wide range of physical systems, including superconductors, quantum spin
liquids, and topological materials. However, investigations of quantum critical
systems also represent one of the most challenging problems in physics, since
highly correlated many-body systems rarely allow for an analytic and tractable
description. Here we present a Lee-Yang theory of quantum phase transitions
including a method to determine quantum critical points which readily can be
implemented within the tensor network formalism and even in realistic
experimental setups. We apply our method to a quantum Ising chain and the
anisotropic quantum Heisenberg model and show how the critical behavior can be
predicted by calculating or measuring the high cumulants of properly defined
operators. Our approach provides a powerful formalism to analyze quantum phase
transitions using tensor networks, and it paves the way for systematic
investigations of quantum criticality in two-dimensional systems.
