Many-Body Model Systems

Luca Salasnich

Kentaro Sugimoto

For many quantum many-body-systems, internal information can be read off as a classical quantity.Based on this idea, this thesis proposes and analyzes two models in which a macroscopic classical-mechanical system and a quantum many-body system are coupled, demonstrating the necessity of modeling the external macroscopic degrees of freedom for the study of quantum many-body systems.The first model focuses on the setup for investigating a two-dimensional helium system with a quartz-crystal microbalance (QCM).This setup is a typical example of a quantum many-body system on a lattice coupled with a classical-mechanically vibrating system.We derive the equation of motion for

Luca Salasnich

Zheng-Yuan Zhang, Dong-Sheng Ding, Bao‐Sen Shi

Quantum simulation has been developed extensively over the past decades, widely applied to different models to explore dynamics in the quantum regime. Rydberg atoms have strong dipole–dipole interactions and interact with each other over a long distance, which makes it straightforward to build many-body interacting quantum systems to simulate specific models. Additionally, neutral atoms are easily manipulated due to their weak interactions. These advantages make Rydberg many-body system an ideal platform to implement quantum simulations. This paper reviews several quantum simulations for different models based on Rydberg many-body systems, including quantum Ising models in one dimension and two dimensions mainly for quantum magnetism, XY model for excitation transport, SSH model for symmetry-protected topological phases, and critical self-organized behaviors in many-body systems. Besides, some challenges and promising directions of quantum simulations based on Rydberg many-body system are discussed in this paper.

Toshiaki Tanaka

We construct a family of quasi-solvable quantum many-body systems by an algebraic method. The models contain up to two-body interactions and have permutation symmetry. We classify these models under the consideration of invariance property. It turns out that this family includes the rational, hyperbolic (trigonometric) and elliptic Inozemtsev models as particular cases.