Abstract

The observation of strongly correlated states in moiré systems has renewed the conceptual interest in magnetic systems with higher SU(4) spin symmetry, e.g., to describe Mott insulators where the local moments are coupled spin–valley degrees of freedom. Here, we discuss a numerical renormalization group scheme to explore the formation of spin–valley ordered and unconventional spin–valley liquid states at zero temperature based on a pseudo-fermion representation. Our generalization of the conventional pseudo-fermion functional renormalization group approach for \({{\mathfrak {s}}}{{\mathfrak {u}}}\)(2) spins is capable of treating diagonal and off-diagonal couplings of generic spin–valley exchange Hamiltonians in the self-conjugate representation of the \({{\mathfrak {s}}}{{\mathfrak {u}}}\)(4) algebra. To achieve proper numerical efficiency, we derive a number of symmetry constraints on the flow equations that significantly limit the number of ordinary differential equations to be solved. As an example system, we investigate a diagonal SU(2)\(_{\text {spin}}\) \(\otimes \) U(1)\(_{\text {valley}}\) model on the triangular lattice which exhibits a rich phase diagram of spin and valley ordered phases.

Graphic Abstract

中文翻译：

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摩尔纹材料中的矩和多重峰

摘要

莫尔系统中强相关态的观察重新激发了对具有较高 SU(4) 自旋对称性的磁系统的概念兴趣，例如，描述局部矩耦合自旋-谷自由度的莫特绝缘体。在这里，我们讨论了一种数值重整化群方案，以基于伪费米子表示探索零温度下自旋谷有序和非常规自旋谷液态的形成。我们对\({{\mathfrak {s}}}{{\mathfrak {u}}}\) (2) 自旋的常规伪费米子泛函重整化群方法的推广能够处理对角线和非对角线耦合\({{\mathfrak {s}}}{{\mathfrak {u}}}\)的自共轭表示中的通用自旋谷交换哈密顿量(4) 代数。为了达到适当的数值效率，我们对流动方程推导出了许多对称约束，这些约束显着限制了要求解的常微分方程的数量。作为一个示例系统，我们研究了对角线 SU(2) \(_{\text {spin}}\) \(\otimes \) U(1) \(_{\text {valley}}\ )三角形晶格，呈现出丰富的自旋和谷序相的相图。

图形摘要