Rigorous existence and location of quantum phase transitions in lattice Hamiltonian systems

We extend the analysis of the class of quantum phase transitions (QPTs) that can be interpreted as condensations in state space, first introduced in [M. Ostilli and C. Presilla, J. Phys. A 54, 055005 (2021)], by generalizing the arguments of [M. Ostilli and C. Presilla, Phys. Rev. Lett. 127, 040601 (2021)] to prove the existence and determine the location (via simple bounds) of QPTs in general one-parameter lattice Hamiltonians. Unlike our original formulation, this extension also encompasses second-order QPTs, for which we provide the explicit example of the transverse-field Ising model. Our analysis suggests that, under conditions typically satisfied in physical contexts, any QPT taking place in lattice systems can be interpreted as a condensation in state space.