Piercing the Dirac spin liquid: From a single monopole to chiral states

TL;DR

This paper investigates the low-energy excitations of the Dirac spin liquid on the kagome lattice, revealing gapless monopole excitations and their coexistence with spinons, using variational Monte Carlo and gauge field modifications.

Contribution

It constructs and analyzes monopole excitations in the Dirac spin liquid, showing their gapless nature and the stability of the Dirac state over chiral states in the kagome lattice.

Findings

Monopole excitations are gapless in the thermodynamic limit.

Chiral states are not stabilized in the nearest-neighbor Heisenberg model.

The Dirac state is the lowest-energy variational wave function.

Abstract

The parton approach for quantum spin liquids gives a transparent description of low-energy elementary excitations, e.g., spinons and emergent gauge-field fluctuations. The latter ones are directly coupled to the hopping/pairing of spinons. By using the fermionic representation of the $U(1)$ Dirac state on the kagome lattice and variational Monte Carlo techniques to include the Gutzwiller projection, we analyse the effect of modifying the gauge fields in the spinon kinematics. In particular, we construct low-energy monopole excitations, which are shown to be gapless in the thermodynamic limit. States with a finite number of monopoles or with a finite density of them are also considered, with different patterns of the gauge fluxes. We show that these chiral states are not stabilized in the Heisenberg model with nearest-neighbor super-exchange couplings, and the Dirac state corresponds to the lowest-energy Ansatz within this family of variational wave functions. Our results support the idea that spinons with a gapless conical spectrum coexist with gapless monopole excitations, even for the spin-1/2 case.