Moments and multiplets in moiré materials

Lasse Gresista; Dominik Kiese; Simon Trebst

doi:10.1140/epjb/s10051-022-00373-2

2023 Impact factor 1.6

Condensed Matter and Complex Systems

Recent Developments in the Functional Renormalization Group Approach to Correlated Electron Systems

Open Access

Eur. Phys. J. B (2022) 95: 119
https://doi.org/10.1140/epjb/s10051-022-00373-2

Regular Article - Computational Methods

A pseudo-fermion functional renormalization group for spin–valley models

Lasse Gresista^a, Dominik Kiese and Simon Trebst

Institute for Theoretical Physics, University of Cologne, 50937, Cologne, Germany

^a gresista@thp.uni-koeln.de

Received: 1 March 2022
Accepted: 22 June 2022
Published online: 30 July 2022

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 $s u$ ${{\mathfrak {s}}}{{\mathfrak {u}}}$ (2) spins is capable of treating diagonal and off-diagonal couplings of generic spin–valley exchange Hamiltonians in the self-conjugate representation of the $s u$ ${{\mathfrak {s}}}{{\mathfrak {u}}}$ (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) $_{spin}$ $_{\text {spin}}$ $\otimes$ $\otimes$ U(1) $_{valley}$ $_{\text {valley}}$ model on the triangular lattice which exhibits a rich phase diagram of spin and valley ordered phases.

© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.