On the relation between k-body interaction and k-particle density

Samuel A. Ocko, Xie Chen, Bei Zeng +4 more

It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While determining which 2-particle density matrices are "N-representable" is a computationally hard problem, all known extreme N-representable 2-particle reduced density matrices arise from a unique N-particle preimage, satisfying a conjecture established in 1972. We present explicit counterexamples to this conjecture through giving Hamiltonians with 2-body interactions which have degenerate ground states that cannot be distinguished by any 2-body operator. We relate the existence of such counterexamples to quantum error correction codes and topologically ordered spin systems.

Klaus Hepp

Bao Cheng-guang

A model of a device is proposed and related theoretical calculation is performed to study the weak interactions among neutral atoms and molecules. In this model 3-body collisions among the neutral particles occur repeatedly in a trap. Results of calculation demonstrate that information on interaction can be obtained by observing the time-dependent densities of the system.

Rutgers University

Stefan Goedecker, Erik Koch

For non-interacting electrons the one-particle density matrix and the related Wannier functions characterize a material as insulating or metallic. Introducing many-body Wannier functions, we show that this characterization can be carried over to interacting systems. In particular, we find that an exponential decay of the density matrix characterizes not only band insulators but also Mott insulators. The properties of the many-body Wannier functions differ, however, from those of the Wannier functions of a non-interacting systems.

Paul G. Federbush