In a spin-1/2 XXZ chain, the sound-velocity shift is determined by derivatives of the spin-chain free energy, and ultrasound attenuation obeys a universal T^3 f(uk/T) scaling in the Luttinger-liquid regime.
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Sound attenuation and velocity shift in antiferromagnetic spin-1/2 chains
In a spin-1/2 XXZ chain, the sound-velocity shift is determined by derivatives of the spin-chain free energy, and ultrasound attenuation obeys a universal T^3 f(uk/T) scaling in the Luttinger-liquid regime.