Spin-valley magnetism on the triangular moiré lattice with SU(4) breaking interactions

Gresista, Lasse; Kiese, Dominik; Scherer, Michael M.

doi:10.1103/physrevb.108.045102

Cited by 2 publications

(2 citation statements)

References 85 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this appendix, we provide a more detailed description of the our semi-classical Monte Carlo implementation. We note that a very similar description (by some of us) for a filling of two instead of one electron per site can be found in [68]. We then conclude this manuscript by presenting additional numerical data elucidating the type of phase transitions separating the disordered and the two ordered states found in the J 2 − J ′ 2 model (see figure 5).…”

Section: Appendix F Semi-classical Monte Carlosupporting

confidence: 68%

Network of chiral one-dimensional channels and localized states emerging in a moiré system

et al. 2023

Self Cite

View full text Add to dashboard Cite

Moiré systems provide a highly tunable platform for engineering band structures and exotic correlated phases. Here, we theoretically study a model for a single layer of graphene subject to a smooth moiré electrostatic potential, induced by an insulating substrate layer. For sufficiently large moiré unit cells, we find that ultra-flat bands coexist with a triangular network of chiral one-dimensional (1D) channels. These channels mediate an effective interaction between localized modes with spin-, orbital- and valley degrees of freedom emerging from the flat bands. The form of the interaction reflects the chiralilty and 1D nature of the network. We study this interacting model within an SU(4) mean-field theory, semi-classical Monte-Carlo simulations, and an SU(4) spin-wave theory, focusing on commensurate order stabilized by local two-site and chiral three-site interactions. By tuning a gate voltage, one can trigger a non-coplanar phase characterized by a peculiar coexistence of three different types of order: ferromagnetic spin order in one valley, non-coplanar chiral spin order in the other valley, and 120° order in the remaining spin and valley-mixed degrees of freedom. Quantum and classical fluctuations have qualitatively different effects on the observed phases and can, for example, create a finite spin-chiralitypurely via fluctuation effects.

show abstract

Section: Appendix F Semi-classical Monte Carlosupporting

confidence: 68%

Network of chiral one-dimensional channels and localized states emerging in a moiré system

et al. 2023

Self Cite

View full text Add to dashboard Cite

show abstract

“…The pseudo-fermion functional renormalization group (PFFRG), which at its core consists of a hierarchy of flow equations for vertex functions, was formulated in a seminal work by Reuther and Wölfle [26,27], and subsequently developed over the years [28][29][30][31][32][33][34][35][36][37][38] to bring much-needed numerical guidance to such frustrated quantum magnets in two [39][40][41][42][43][44][45][46][47][48][49][50][51] and three spatial dimensions [43,[52][53][54][55][56][57][58][59][60][61][62][63][64][65][66]. Much technical understanding has been developed over the past fifteen years including ways to reduce the number of flow equations by symmetry-optimization [67], to reliably distinguish the formation of quantum spin liquids versus the longrange magnetic order, to expand the approach to the limits of large S [68] and large N …”

Section: Introductionmentioning

confidence: 99%

Pseudo-fermion functional renormalization group for spin models

Müller,

Kiese,

Niggemann

et al. 2024

Rep. Prog. Phys.

Self Cite

View full text Add to dashboard Cite

For decades, frustrated quantum magnets have been a seed for scientific progress and innovation in condensed matter. As much as the numerical tools for low-dimensional quantum magnetism have thrived and improved in recent years due to breakthroughs inspired by quantum information and quantum computation, higher-dimensional quantum magnetism can be considered as the final frontier, where strong quantum entanglement, multiple ordering channels, and manifold ways of paramagnetism culminate. At the same time, efforts in crystal synthesis have induced a significant increase in the number of tangible frustrated magnets which are generically three-dimensional in nature, creating an urgent need for quantitative theoretical modeling. We review the pseudo-fermion (PF) and pseudo-Majorana (PM) functional renormalization group (FRG) and their specific ability to address higher-dimensional frustrated quantum magnetism. First developed more than a decade ago, the PFFRG interprets a Heisenberg model Hamiltonian in terms of Abrikosov pseudofermions, which is then treated in a diagrammatic resummation scheme formulated as a renormalization group flow of $m$-particle pseudofermion vertices. The article reviews the state of the art of PFFRG and PMFRG and discusses their application to exemplary domains of frustrated magnetism, but most importantly, it makes the algorithmic and implementation details of these methods accessible to everyone. By thus lowering the entry barrier to their application, we hope that this review will contribute towards establishing PFFRG and PMFRG as the numerical methods for addressing frustrated quantum magnetism in higher spatial dimensions.

show abstract

Spin-valley magnetism on the triangular moiré lattice with SU(4) breaking interactions

Cited by 2 publications

References 85 publications

Network of chiral one-dimensional channels and localized states emerging in a moiré system

Network of chiral one-dimensional channels and localized states emerging in a moiré system

Pseudo-fermion functional renormalization group for spin models

Contact Info

Product

Resources

About