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

Abstract

The Grüneisen 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 analogue 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 $\lambda$ non-linearly. Furthermore, we demonstrate the breakdown of the Hellmann-Feynman theorem in the thermodynamic limit at any QCP. We showcase our approach using the quantum 1D Ising model with 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.

5 pages, 3 figures, comments are wellcome!

References in corpus (5)

• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Theory of a continuous Mott transition in two dimensions
• Scaling theory of the Mott transition and breakdown of the Grüneisen scaling near a finite-temperature critical end point
• Multi-partite entanglement and quantum phase transition in the one-, two-, and three-dimensional transverse field Ising model
• Entropy accumulation near quantum critical points: effects beyond hyperscaling

Cited by in corpus (3)

• Quasilocal entanglement across the Mott-Hubbard transition
• Maxwell relation between entropy and atom-atom pair correlation
• Cellular Griffiths-like phase