Critical Casimir forces from the equation of state of quantum critical systems

TL;DR

This paper establishes a theoretical connection between the critical Casimir force in classical systems and the internal energy of quantum critical systems, providing methods to estimate and experimentally realize these forces.

Contribution

It introduces a framework linking classical Casimir forces to quantum critical points, enabling quantitative predictions and experimental protocols.

Findings

Quantitative estimates of critical Casimir forces from quantum Monte Carlo simulations.

Analysis of symmetry-related quantum critical points to derive classical scaling functions.

Proposals for experimental realization using cold-atom and solid-state systems.

Abstract

The mapping between a classical length and inverse temperature as imaginary time provides a direct equivalence between the Casimir force of a classical system in $D$ dimensions and internal energy of a quantum system in $d$$=$$D$$-$$1$ dimensions. The scaling functions of the critical Casimir force of the classical system with periodic boundaries thus emerge from the analysis of the symmetry related quantum critical point. We show that both non-perturbative renormalization group and quantum Monte Carlo analysis of quantum critical points provide quantitative estimates for the critical Casimir force in the corresponding classical model, giving access to widely different aspect ratios for the geometry of confined systems. In the light of these results we propose protocols for the experimental realization of critical Casimir forces for periodic boundaries through state-of-the-art cold-atom and solid-state experiments.