Competing magnetic orders and spin liquids in two- and three-dimensional kagome systems: A pseudo-fermion functional renormalization group perspective

TL;DR

This paper uses a pseudo-fermion functional renormalization group method to explore how various exchange interactions influence magnetic orders and spin liquids in kagome lattice systems, revealing complex phase diagrams.

Contribution

It introduces and applies a pf-FRG approach to study extended exchange interactions in kagome systems, providing detailed phase diagrams and validating the method against high-temperature series expansions.

Findings

Next-nearest neighbor couplings induce diverse magnetic orders.

Additional spin liquid regimes emerge with extended interactions.

pf-FRG shows excellent agreement with series expansions.

Abstract

Quantum magnets on kagome lattice geometries in two and three spatial dimensions are archetypal examples of spin systems in which geometric frustration inhibits conventional magnetic ordering and instead benefits the emergence of long-range entangled spin liquids at low temperature. Here we employ a recently developed pseudo-fermion functional renormalization group (pf-FRG) approach to study the low-temperature quantum magnetism of kagome and hyperkagome spin systems with exchange interactions beyond the nearest neighbor coupling. We find that next-nearest neighbor couplings stabilize a variety of magnetic orders as well as induce additional spin liquid regimes giving rise to rather rich phase diagrams, which we characterize in detail. On a technical level, we find that the pf-FRG approach is in excellent quantitative agreement with high-temperature series expansions over their range of validity and it exhibits a systematic finite-size convergence in the temperature regime below. We discuss notable advantages and some current limitations of the pf-FRG approach in the ongoing search for unconventional forms of quantum magnetism.