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Pseudo-fermion functional renormalization group for spin models.

Tobias Müller1, Dominik Kiese2, Nils Niggemann3,4,5

  • 1Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, Würzburg D-97074, Germany.

Reports on Progress in Physics. Physical Society (Great Britain)
|January 19, 2024
PubMed
Summary
This summary is machine-generated.

Pseudo-fermion (PF) and pseudo-Majorana (PM) functional renormalization group (FRG) methods offer new ways to study complex, higher-dimensional frustrated quantum magnets. These techniques aim to make advanced numerical modeling more accessible for condensed matter research.

Keywords:
frustrated magnetismfunctional renormalization groupquantum many-body methodsquantum spin liquidsspin modelsstrongly correlated systems

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Area of Science:

  • Condensed matter physics
  • Quantum magnetism
  • Computational physics

Background:

  • Frustrated quantum magnets are crucial for scientific progress.
  • Advances in quantum information have improved low-dimensional magnetism tools.
  • Higher-dimensional quantum magnetism presents unique challenges like entanglement and multiple ordering channels.

Purpose of the Study:

  • To review pseudo-fermion (PF) and pseudo-Majorana (PM) functional renormalization group (FRG) methods.
  • To highlight their applicability to higher-dimensional frustrated quantum magnetism.
  • To make the algorithmic and implementation details of PFFRG and PMFRG accessible.

Main Methods:

  • The review focuses on pseudo-fermion functional renormalization group (PFFRG) and pseudo-Majorana functional renormalization group (PMFRG).
  • PFFRG models Heisenberg Hamiltonians using Abrikosov pseudofermions.
  • It employs a renormalization group flow of m-particle pseudofermion vertices for diagrammatic resummation.

Main Results:

  • The article provides a state-of-the-art review of PFFRG and PMFRG.
  • It discusses applications in exemplary domains of frustrated magnetism.
  • Algorithmic and implementation details are made accessible to lower the entry barrier for researchers.

Conclusions:

  • PFFRG and PMFRG are powerful numerical methods for studying frustrated quantum magnetism.
  • Increased accessibility is expected to establish these methods for higher-dimensional systems.
  • This work aims to foster wider adoption and application of these advanced computational techniques.