Gr\"uneisen parameter as an entanglement compass and the breakdown of the Hellmann-Feynman theorem

TL;DR

This paper introduces a quantum analogue of the Gr"uneisen ratio to detect quantum phase transitions through entanglement, revealing the breakdown of the Hellmann-Feynman theorem at critical points.

Contribution

It proposes a new entanglement-based measure for quantum phase transitions and demonstrates the breakdown of the Hellmann-Feynman theorem at QCPs.

Findings

Quantum entanglement measure signals QPTs.

Hellmann-Feynman theorem fails at QCPs.

Application to 1D Ising model and quantum computer.

Abstract

The Gr\"uneisen 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.