Universal and non-universal facets of quantum critical phenomena unveiled along the Schmidt decomposition theorem

• URL: http://arxiv.org/abs/2512.11093v1
• Date: Thu, 11 Dec 2025 20:09:23 GMT
• Title: Universal and non-universal facets of quantum critical phenomena unveiled along the Schmidt decomposition theorem
• Authors: Samuel M. Soares, Lucas Squillante, Henrique S. Lima, Constantino Tsallis, Mariano de Souza,
• Abstract summary: We investigate the influence of the spin magnitude $S$ on the quantum Grneisen parameter $0textK_q$ right at critical points (CPs) for the 1D Ising model under a transverse magnetic field.<n>Our findings unveil both universal and non-universal aspects of quantum criticality in terms of $0textK_q$ and $S_q$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the influence of the spin magnitude $S$ on the quantum Grüneisen parameter $Γ^{0\text{K}}_q$ right at critical points (CPs) for the 1D Ising model under a transverse magnetic field. Our findings are fourfold: $\textit{i)}$ for higher $S$, $Γ^{0\text{K}}_q$ is increased, but remains finite, reflecting the enhancement of the Hilbert space dimensionality; $\textit{ii)}$ the Schmidt decomposition theorem recovers the extensivity of the nonadditive $q$-entropy $S_q$ only for a $\textit{special}$ value of the entropic index $q$; $\textit{iii)}$ the universality class in the frame of $S_q$ depends only on the symmetry of the system; $\textit{iv)}$ we propose an experimental setup to explore finite size effects in connection with the Hilbert space occupation at CPs. Our findings unveil both universal and non-universal aspects of quantum criticality in terms of $Γ^{0\text{K}}_q$ and $S_q$.

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