Quantum Locality for a Pair of Interacting Systems

Travis Norsen

M. Dugić, J. Jeknić-Dugić

We discuss the quantum locality (non-transfer of information) for a pair of mutually interacting systems, and point out the relaxed locality. The models fulfilling the relaxed locality condition can serve as a guide for quantum engineers in designing quantum-information hardware.

Shang-Shu Li, Zi-Yong Ge, Heng Fan

Quantum simulation in experiments of many-body systems may bring new phenomena which are not well studied theoretically. Motivated by a recent work of quantum simulation on a superconducting ladder circuit, we investigate the rung-pair localization of the Bose-Hubbard ladder model without quenched disorder. Our results show that, in the hard-core limit, there exists a rung-pair localization both at the edges and in the bulk. Using the center-of-mass frame, the two-particle system can be mapped to an effective single-particle system with an approximate sublattice symmetry. Under the condition of the hard-core limit, the effective system is forced to have a defect at the left edge leading to a zero-energy flatband, which is the origin of the rung-pair localization. We also study the multiparticle dynamics of the Bose-Hubbard ladder model, which is beyond the single-particle picture. In this case, we find that the localization can still survive despite the existence of interaction between the pairs. Moreover, the numerical results show that the entanglement entropy exhibits a long-time logarithmic growth and the saturated values satisfy a volume law. This phenomenon implies that the interaction plays an important role during the dynamics, although it cannot break the localization. Our results reveal another interesting type of disorder-free localization related to a zero-energy flatband, which is induced by on-site interaction and specific lattice symmetry.

D. A. Slavnov

J.-B. Bru, W. de Siqueira Pedra, Alan Ramer dos Santos

Abstract Quantum interactions exchanging different types of particles play a pivotal rôle in quantum many-body theory, but they are not sufficiently investigated from a mathematical perspective. Here, we consider a system made of two fermions and one boson, in order to study the effect of such an off-diagonal interaction term, having in mind the physics of cuprate superconductors. Additionally, our model also includes a generalized Hubbard interaction (i.e., a general local repulsion term for the fermions). Regarding pairing, exponentially localized dressed bound fermion pairs are shown to exist, and their effective dispersion relation is studied in detail. Scattering properties of the system are derived for two channels: the unbound and bound pair channels. We give particular attention to the regime of very large on-site (Hubbard) repulsions because this situation is relevant for cuprate superconductors.

Gregg S. Jaeger