Strongly correlated flat-band systems: Ground state and low-temperature properties

强相关平带系统：基态和低温特性

• 批准号: 224226278
• 负责人: Professor Dr. Johannes Richter
• 金额: --
• 依托单位: Institut für Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/224226278?language=en
• 关键词: Strongly; correlated; flat; band; systems

Strongly correlated flat-band systems may exhibit interesting phenomena such as Wigner crystallization, high-temperature fractional quantum Hall states, macroscopic magnetization jumps, or magnetic-field induced spin-Peierls instabilities. Moreover, they provide a route to ferromagnetism in the Hubbard model. In this project, we consider a class of strongly correlated frustrated systems with a completely dispersionless (flat) one-particle band (flat-band systems), for which exact many-body localized ground states can be constructed. The corresponding low-energy degrees of freedom of the quantum model can be described by classical lattice-gas models. We apply this concept on quantum spin systems described by the Heisenberg model as well as on electron systems described by the Hubbard model. The effective classical lattice-gas models can be used to calculate the low-temperature thermodynamics of the corresponding quantum models. For Hubbard systems the localized states lead to ground-state ferromagnetism which can be considered as a Pauli correlated percolation problem. The relaxation of the flat-band condition may lead to new quantum effects.

强关联平带系统可能会表现出有趣的现象，如维格纳结晶，高温分数量子霍尔态，宏观磁化跳变，或磁场诱导的自旋佩尔斯不稳定性。此外，它们提供了一条通往哈伯德模型铁磁性的途径。在这个项目中，我们考虑了一类具有完全无色散（平坦）单粒子带的强关联阻挫系统（平带系统），对于这类系统，可以构造精确的多体局域基态。量子模型的相应低能自由度可以用经典格子气体模型来描述。我们应用这个概念的量子自旋系统所描述的海森堡模型以及电子系统所描述的哈伯德模型。有效的经典格气模型可以用来计算相应量子模型的低温热力学。对于Hubbard系统，局域态导致基态铁磁性，这可以被认为是一个泡利相关渗流问题。平带条件的松弛可能导致新的量子效应。