Gauge flux generations of weakly magnetized Dirac spin liquid in a kagom\'{e} lattice

TL;DR

This paper investigates how weak magnetic fields induce gauge flux in a Dirac spin liquid on a kagome lattice, revealing spontaneous flux generation and resulting magnetic order with gapless excitations.

Contribution

It demonstrates the non-perturbative generation of uniform gauge flux and the resulting magnetic order in a Dirac spin liquid using renormalized mean-field theory.

Findings

Weak magnetic fields induce internal U(1) gauge flux.

Spontaneous uniform gauge flux leads to spinon Landau levels.

The resulting state is an ordered antiferromagnet with Goldstone modes.

Abstract

Inspired by the recent progress on the Dirac spin liquid and the kagom\'{e} lattice antiferromagnets, we revisit the U(1) Dirac spin liquid on the kagom\'{e} lattice and consider the response of this quantum state to the weak magnetic field by examining the matter-gauge coupling. Even though the system is in the strong Mott insulating regime, the Zeeman coupling could induce the internal U(1) gauge flux with the assistance of the Dzyaloshinskii-Moriya interaction. In addition to the perturbatively-induced non-uniform flux from the microscopic interactions, the system spontaneously generates the uniform U(1) gauge flux in a non-perturbative fashion to create the spinon Landau levels and thus gains the kinetic energy for the spinon matters. Renormalized mean-field theory is employed to validate these two flux generation mechanisms. The resulting state is argued to be an ordered antiferromagnet with the in-plane magnetic order, and the gapless Goldstone mode behaves like the gapless gauge boson and the spinons appear at higher energies. The dynamic properties of this antiferromagnet, and the implication for other matter-gauge-coupled systems are discussed.