Theoretical studies of the Mott transition in extended Hubbard models

该项目的目的是了解费米液体和莫特绝缘体之间的连续相变，这是由皇家霍洛威大学的约翰·桑德斯（John Saunders）在He-3原子沉积在He-4原子三角形晶格上的系统中实验观察到的。这种莫特过渡发生在填充4/7时，预计将用扩展的哈伯德模型在三角形晶格上描述。Miki将首先使用从粒子平均场理论（如Kotliar-Ruckenstein理论）来研究这个模型。下一步，我们将分析由从粒子结构引起的规范场波动的影响。正如Senthil在具有纯现场排斥的Hubbard模型的背景下所证明的那样，这些波动产生了一个临界非费米液态，它遵循与Varma边际费米液态相同的标度定律。一个重要的问题是，像在氦系统中看到的那样，对平移对称的额外破坏是否会产生新的普遍行为。

The aim of the project is to understand the continuous phase transition between a Fermi liquid and a Mott insulator observed experimentally by John Saunders at Royal Holloway in a system of He-3 atoms deposited on a triangular lattice of He-4 atoms. This Mott transition takes place at a filling of 4/7 and is expected to be described by an extended Hubbard model on the triangular lattice. Miki will first study this model by using slave-particle mean-field theories, such as the Kotliar-Ruckenstein theory. As a next step we will analyse the effects of fluctuations of the gauge fields that arise from the slave-particle construction. As demonstrated by Senthil in the context of the Hubbard model with pure on-site repulsion, these fluctuations give rise to a critical non-Fermi liquid state that obeys the same scaling laws as Varma's marginal Fermi liquid. One important question is whether the additional breaking of translational symmetry, as seen in the helium system, can give rise to novel universal behaviour.