Raman signature of the U(1) Dirac spin-liquid state in spin-1/2 kagome system

TL;DR

This paper investigates the Raman scattering signatures of the U(1) Dirac spin-liquid state in the spin-1/2 kagome lattice, revealing broad continua with specific power-law behaviors and a characteristic singularity linked to emergent gauge fields.

Contribution

It provides a detailed theoretical analysis of the Raman response in the U(1) Dirac spin-liquid state on the kagome lattice, including the role of spin chirality and emergent gauge fields.

Findings

Raman intensity profiles show broad continua with power-law behavior.

The A_{2g} channel exhibits a 1/ω singularity due to gauge field excitations.

The Raman response is invariant under in-plane rotations in the kagome lattice.

Abstract

We followed the Shastry--Shraiman formulation of Raman scattering in Hubbard systems and considered the Raman intensity profile in the spin-1/2 "perfect" kagome lattice herbertsmithite ZnCu_3(OH)_6Cl_2, assuming the ground state is well-described by the U(1) Dirac spin-liquid state. In the derivation of the Raman T-matrix, we found that the spin chirality term appears in the A_{2g} channel in the kagome lattice at the t^4/(\omega_i-U)^3 order, but (contrary to the claims by Shastry and Shraiman) vanishes in the square lattice to that order. In the ensuing calculations on the spin-1/2 kagome lattice, we found that the Raman intensity profile in the E_g channel is invariant under an arbitrary rotation in the kagome plane, and that in all (A_{1g}, E_g, and A_{2g}) symmetry channels the Raman intensity profile contains broad continua that display power-law behaviors at low energy, with exponent approximately equal to 1 in the A_{2g} channel and exponent approximately equal to 3 in the E_g and the A_{1g} channels. For the A_{2g} channel, the Raman profile also contains a characteristic 1/\omega singularity, which arose in our model from an excitation of the emergent U(1) gauge field.