Spinon-Phonon Interaction in Algebraic Spin Liquids

Abstract

Motivated by a search for experimental probes to access the physics of fractionalized excitations called spinons in a spin liquids, we study the interaction of spinons with lattice vibrations. We consider the case of algebraic spin liquid, when spinons have fermionic statistics and a Dirac-like dispersion. We establish the general procedure for deriving spinon-phonon interactions which is based on a symmetry considerations. The procedure is illustrated for four different algebraic spin liquids: pi-flux and staggered-flux phases on a square lattice, pi-flux phase on a kagome lattice, and zero flux phase on a honeycomb lattice. Although the low energy description is similar for all these phases, different underlying symmetry group leads to a distinct form of spinon-phonon interaction Hamiltonian. The explicit form of the spinon-phonon interaction is used to estimate the attenuation of ultrasound in an algebraic spin liquid. The perspectives of the sound attenuation as probe of spinons are discussed.

18 pages, 3 figures, 8 tables

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• Probing signatures of fractionalization in candidate quantum spin liquid Cu2IrO3 via anomalous Raman scattering
• Infrared phonons as a probe of a spin-liquid states in herbertsmithite ZnCu3(OH)6Cl2
• Unified picture of superconductivity and magnetism in CeRh${}_2$As${}_2$
• Theory of Dirac Spin-Orbital Liquids: monopoles, anomalies, and applications to $SU(4)$ honeycomb models
• Elastic constants and ultrasound attenuation in the spin-liquid phase of Cs${}_2$CuCl${}_4$
• Inversion-asymmetric itinerant antiferromagnets by the space group symmetry
• Many-body theory of magneto-elasticity in one dimension
• Sound attenuation in the hyperhoneycomb Kitaev spin liquid
• Spin-lattice Coupling in U(1) Quantum Spin Liquids
• Tuning magnetic interactions with nonequilibrium optical phonon populations: a theoretical study
• Phonon anomalies and critical scaling in the spin-$1/2$ trimer chain Na${}_2$Cu${}_3$Ge${}_4$O${}_{12}$