Unnecessary quantum criticality in $SU(3)$ kagome magnets

TL;DR

This paper investigates $SU(3)$ kagome lattice spin systems, proposing that the algebraic spin liquid phase is an unnecessary quantum critical point within a single phase, challenging the conventional understanding of such critical states.

Contribution

The study demonstrates that the $SU(3)$ kagome magnet's Dirac spin liquid is an unnecessary quantum critical point, providing new insights into quantum criticality and phase structure in frustrated magnets.

Findings

DSL is a quantum critical point accessible by tuning a microscopic parameter.

The low energy DSL is within a single phase, not a phase transition.

Emergent symmetry and anomalies support the unnecessary criticality conjecture.

Abstract

Algebraic/Dirac spin liquids (DSLs) are a class of critical quantum ground states that do not have a quasi-particle description. DSLs and related spin liquid phases often arise in strongly frustrated quantum spin systems, in which strong correlations and quantum fluctuations among constituent spins persist down to zero temperature. In this work, we analyze Mott insulating phases of $SU(3)$ fermions on a kagome lattice which may realize a DSL phase, described at low energies by $(2 + 1)d$ quantum electrodynamics (QED$_3$) with $N_f=6$ Dirac fermions. By analyzing the action of physical symmetries on the operators of the QED$_3$ theory, we conclude that the low energy DSL is a quantum critical point that can be accessed by tuning a single microscopic parameter. Aided by the emergent symmetry and anomalies of the low energy effective theory, we conjecture and present supporting arguments that the $SU(3)$ Kagome magnet DSL is an unnecessary quantum critical point, lying completely within a single phase.