Pseudo-fermion functional renormalization group for spin models.
Tobias Müller, Dominik Kiese, Nils Niggemann, Björn Sbierski, Johannes Reuther, Simon Trebst, Ronny Thomale, Yasir Iqbal
Author Information
Tobias Müller: Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, Würzburg D-97074, Germany. ORCID
Dominik Kiese: Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, United States of America. ORCID
Nils Niggemann: Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, D-14195 Berlin, Germany. ORCID
Björn Sbierski: Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstraße 37, München D-80333, Germany. ORCID
Johannes Reuther: Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, D-14195 Berlin, Germany.
Simon Trebst: Institut für Theoretische Physik, Zülpicher Straße 77a, Universität zu Köln, 50937 Köln, Germany. ORCID
Ronny Thomale: Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, Würzburg D-97074, Germany. ORCID
Yasir Iqbal: Department of Physics and Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), Indian Institute of Technology Madras, Chennai 600036, India. ORCID
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-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.
