Universal features of non-analytical energy storage in quantum critical quantum batteries

TL;DR

The paper addresses how quantum phase transitions affect energy storage in free-fermion quantum batteries during sudden quenches. It develops a Dirac-cone-based, low-energy framework to predict universal non-analyticities in the stored energy, dependent on the dimensionality, and validates these predictions with lattice models Ising chain and Haldane model. The main contributions are a general ΔE_{dD} description whose odd/even dimensionality dictates a jump or a logarithmic divergence in the d-th derivative at criticality, along with lattice-model confirmation and the observation that energy storage in the Haldane model follows the topological phase diagram. These results highlight a fundamental link between quantum criticality and energetic response, revealing both stability challenges near critical points and opportunities for enhanced control and topological-phase sensing via energy metrics.

Abstract

Quantum batteries are quantum mechanical systems able to store and release energy in a controlled fashion. Among them, a special role is played by quantum structures defined as networks of two-level systems. In this context, it has recently been shown that the energy stored in free fermion quantum batteries is sensitive to the quantum phase diagram of the battery itself. This sensitivity is relevant for stabilizing the stored energy and designing optimal charging protocols. In this article, we explore universal charging behaviors of free fermion quantum batteries across quantum phase transitions. We first analyze a Dirac cone-like model to extract general features. Then, we verify our findings by means of two relevant lattice models, namely the Ising chain in a transverse field and the Haldane model.

Figures (6)

• Figure 1: First derivative of the stored energy in the Ising chain with respect to the transverse field as a function of the initial magnetic field $h_0$.
• Figure 2: Honeycomb lattice of the Haldane model.
• Figure 3: Energy stored in the Haldane model as function of $t_2^{(A)}$ for $t_1 = 0.5$ (green), $t_1 = 0.8$ (red), $t_1 = 1.5$ (purple), $t_1 = 3$ (brown) and $t_1 = 5$ (pink) with fixed $\delta = 0.1$. The red dotted lines represent the critical $t_2$ values for the evolution Hamiltonian, while the different colors indicate the phase of the model according to the Chern number's value, as represented under the plot: topological phase with $C = -1$ (green region), topological phase with $C = 1$ (red region) and trivial phase with $C = 0$ (white region)
• Figure 4: Second derivative of the energy stored in the Haldane model as a function of $t_2^{(A)}$.
• Figure 5: Energy stored in the 1-D Dirac model as function of $m_A$ for $\delta = 2$ (blue curve) and jump in its first derivative with respect to $m_A$ as function of $m_A$ (orange curve).