Discrete quantum theory

V. I. Kukulin, O. A. Rubtsova

Lay Nam Chang, Zachary Lewis, Djordje Minić +1 more

Zhengqian Cheng, Chris A. Marianetti

Here we propose the variational discrete action theory (VDAT) to study the ground state properties of quantum many-body Hamiltonians. VDAT is a variational theory based on the sequential product density matrix (SPD) ansatz, characterized by an integer N, which monotonically approaches the exact solution with increasing N. To evaluate the SPD, we introduce a discrete action and a corresponding integer time Green's function. We use VDAT to exactly evaluate the SPD in two canonical models of interacting electrons: the Anderson impurity model and the d=∞ Hubbard model. For the latter, we evaluate N=2-4, where N=2 recovers the Gutzwiller approximation (GA), and we show that N=3, which exactly evaluates the Gutzwiller-Baeriswyl wave function, provides a truly minimal yet precise description of Mott physics with a cost similar to that of the GA. VDAT is a flexible theory for studying quantum Hamiltonians, competing both with state-of-the-art methods and simple, efficient approaches all within a single framework.

Richard M. Friedberg, T. D. Lee

Martin Leckey

This paper presents a new modified quantum mechanics, Critical Complexity Quantum Mechanics, which includes a new account of wavefunction collapse. This modified quantum mechanics is shown to arise naturally from a fully discrete physics, where all physical quantities are discrete rather than continuous. I compare this theory with the spontaneous collapse theories of Ghirardi, Rimini, Weber and Pearle and discuss some implications of the theory for a realist view of the quantum realm.

Richard M. Friedberg, T.D. Lee