Grüneisen parameter as an entanglement compass and the breakdown of the Hellmann-Feynman theorem
Lucas Squillante, L. S. Ricco, Aniekan Magnus Ukpong, Roberto E. Lagos-Monaco, A. C. Seridonio, M De Souza
Abstract
The Gr\"uneisen ratio $\mathrm{\ensuremath{\Gamma}}$, 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 $\mathrm{\ensuremath{\Gamma}}$ cannot be employed. We propose a quantum analog to $\mathrm{\ensuremath{\Gamma}}$ that computes entanglement as a function of a tuning parameter $\ensuremath{\lambda}$ and show that QPTs take place only for systems in which the ground-state energy depends on $\ensuremath{\lambda}$ 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.