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Multiloop Functional Renormalization Group for Quantum Spin Systems

Date and Time: Tuesday, December 14, 2021, 01:30pm -
Location: Zoom

Speaker: Dominik Kiese (University of Cologne)


The intriguing possibility of realizing elusive spin liquid states in frustrated quantum magnets, featuring long-range entanglement and fractionalized quasi-particle excitations, continues to be an active subject of modern condensed matter research. Determining their ground state phase diagrams from numerical approaches, however, turns out to be quite difficult. While exact diagonalization and tensor network algorithms are usually limited to one and two dimensional systems, due to unfavorable scaling of numerical complexity in higher dimensions, quantum Monte Carlo simulations, where large system sizes are within computational reach, suffer from the notorious sign problem.

In recent years, the pseudo-fermion functional renormalization group (pf-FRG) method, a Feynman diagram based approach originally developed by Reuther and Woelfle, has turned out to be a powerful and versatile tool to investigate ground state phase diagrams of quantum spin models. Yet, the intrinsic consistency and hence validity of the method, as well as its numerical accuracy, have not caught as much attention as its application to paradigmatic models of frustrated magnetism in both two and three dimensional systems. Here, we develop and apply a multiloop truncated version of pf-FRG at zero temperature, which fully incorporates self-energy and inter-channel feedback for the flow of running couplings, and thus asymptotically reaches the accuracy of the parquet approximation. We will demonstrate, how this methodological extension requires a critical reevaluation of the numerical implementation in order to obtain RG flows with unprecedented accuracy.

Host:  David Vanderbilt

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