Grüneisen parameter as an entanglement compass and the breakdown of the Hellmann-Feynman theorem - Squillante, Lucas [UNESP]; Ricco, Luciano S.; Ukpong, Aniekan Magnus; Lagos-Monaco, Roberto E. [UNESP]; Seridonio, Antonio C. [UNESP]; De Souza, Mariano [UNESP] (American Physical Society (APS), 2023)
The Grüneisen ratio Γ, i.e., the singular part of the ratio of thermal expansion to the specific heat, has been broadly employed to explore both finite T and quantum critical points (QCPs). For a genuine quantum phase transition (QPT), thermal fluctuations are absent and thus the thermodynamic Γ cannot be employed. We propose a quantum analog to Γ that computes entanglement as a function of a tuning parameter λ and show that QPTs take place only for systems in which the ground-state energy depends on λ nonlinearly. Furthermore, we demonstrate the breakdown of the Hellmann-Feynman theorem in the thermodynamic limit at any QCP. We showcase our approach using the quantum one-dimensional Ising model with a transverse field and Kane's quantum computer. The slowing down of the dynamics and thus the creation of massclose to any QCP/QPT is also discussed.