Grüneisen parameter as an entanglement compass and the breakdown of the Hellmann-Feynman theorem

The Gruneisen ratio Gamma, 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 Gamma cannot be employed. We propose a quantum analog to Gamma that computes entanglement as a function of a tuning parameter lambda and show that QPTs take place only for systems in which the ground-state energy depends on lambda 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 mass close to any QCP/QPT is also discussed.

Automated summary

This article proposes a quantum analog to the Gruneisen ratio Gamma, which computes entanglement as a function of a tuning parameter lambda and investigates quantum critical points. The authors demonstrate that quantum phase transitions only occur when the ground-state energy depends nonlinearly on lambda. Furthermore, the breakdown of the Hellmann-Feynman theorem at any quantum critical point is shown.