Computation of quantum phase transitions by reduced-density-matrix mechanics

Quantum phase transitions are explored with reduced-density-matrix (RDM) mechanics. While in wave mechanics the quantum phase transition is identified by a crossing or avoided crossing between ground- and excited-state energies, in RDM mechanics the transition is characterized by movement of the ground-state two-electron RDM (2-RDM) along the boundary of the convex set of 2-RDMs between regions with dramatically different expectation values (order parameters) of one or more operators. With recent advances the ground-state 2-RDM can be directly computed without the many-particle wave function by variational optimization of the energy with the 2-RDM [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)]. Because the variational calculation of the 2-RDM does not depend on a reference wave function, it can accurately predict the energies and properties of a system both near and far from the quantum phase transition.