Functional renormalization group for frustrated magnets with nondiagonal spin interactions

Abstract

In the field of quantum magnetism, the advent of numerous spin-orbit assisted Mott insulating compounds, such as the family of Kitaev materials, has led to a growing interest in studying general spin models with non-diagonal interactions that do not retain the SU(2) invariance of the underlying spin degrees of freedom. However, the exchange frustration arising from these non-diagonal and often bond-directional interactions for two- and three-dimensional lattice geometries poses a serious challenge for numerical many-body simulation techniques. In this paper, we present an extended formulation of the pseudo-fermion functional renormalization group that is capable of capturing the physics of frustrated quantum magnets with generic (diagonal and off-diagonal) two-spin interaction terms. Based on a careful symmetry analysis of the underlying flow equations, we reveal that the computational complexity grows only moderately, as compared to models with only diagonal interaction terms. We apply the formalism to a kagome antiferromagnet which is augmented by general in-plane and out-of-plane Dzyaloshinskii-Moriya (DM) interactions, as argued to be present in the spin liquid candidate material herbertsmithite. We calculate the complete ground state phase diagram in the strength of in-plane and out-of-plane DM couplings, and discuss the extended stability of the spin liquid of the unperturbed kagome antiferromagnet in the presence of these couplings.

arXiv comment19 pages, 6 figures

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• Benchmark Calculations of Multiloop Pseudofermion fRG
• Feasibility of Kitaev quantum spin liquids in ultracold polar molecules
• Bilinear Majorana representations for spin operators with spin magnitudes $S>1/2$
• Moments and multiplets in moiré materials: A pseudo-fermion functional renormalization group for spin-valley models
• Ground-State Phase Diagram of the Kitaev-Heisenberg Model on a Three-dimensional Hyperhoneycomb Lattice
• A pseudofermion functional renormalization group study of dipolar-octupolar pyrochlore magnets
• Pseudo-fermion functional renormalization group with magnetic fields
• The SpinParser software for pseudofermion functional renormalization group calculations on quantum magnets
• Schwinger boson study of the $J_1$-$J_2$-$J_3$ kagome Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions
• Crystallography-driven molecularization of a two-dimensional spin-$3/2$ magnet