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The mechanism of not diverging Gr{u}neisen parameter in the quantum critical heavy-fermion quasicrystal (QC) Yb$_{15}$Al$_{34}$Au$_{51}$ is analyzed. We construct the formalism for calculating the specific heat $C_V(T)$, the thermal-expansion coefficient $alpha(T)$, and the Gr{u}neisen parameter $Gamma(T)$ near the quantum critical point of the Yb valence transition. By applying the framework to the QC, we calculate $C_V(T)$, $alpha(T)$, and $Gamma(T)$, which explains the measurements. Not diverging $Gamma(T)$ is attributed to the robustness of the quantum criticality in the QC under pressure. The difference in $Gamma(T)$ at the lowest temperature between the QC and approximant crystal is shown to reflect the difference in the volume derivative of characteristic energy scales of the critical Yb-valence fluctuation and the Kondo temperature. Possible implications of our theory to future experiments are also discussed.
Complete expressions of the thermal-expansion coefficient $alpha$ and the Gr{u}neisen parameter $Gamma$ are derived on the basis of the self-consistent renormalization (SCR) theory. By considering zero-point as well as thermal spin fluctuation under
The elastic property of quantum critical quasicrystal (QC) Yb$_{15}$Al$_{34}$Au$_{51}$ is analyzed theoretically on the basis of the approximant crystal (AC) Yb$_{14}$Al$_{35}$Au$_{51}$. By constructing the realistic effective model in the AC, we eva
Using Hartree-Fock-Bogoliubov (HFB) approach we obtained analytical expressions for thermodynamic quantities of the system of triplons in spin gapped quantum magnets such as magnetization, heat capacity and the magnetic Gr{u}neisen parameter $Gamma_H
We report on ac magnetic susceptibility measurements under pressure of the Au-Al-Yb alloy, a crystalline approximant to the icosahedral quasicrystal that shows unconventional quantum criticality. In describing the susceptibility as $chi(T)^{-1} - chi
Quasicrystals are metallic alloys that possess long-range, aperiodic structures with diffraction symmetries forbidden to conventional crystals. Since the discovery of quasicrystals by Schechtman et al. at 1984 (ref. 1), there has been considerable pr