Collective dynamics versus entanglement in quantum battery performance

TL;DR

The paper addresses whether enhanced charging in many-body quantum batteries is due to quantum correlations or coherent collective dynamics. They build a model with a quantum battery and a charger, with varying kappa-local interactions and norm-constrained (fair) charging; they measure energy storage W(t), instantaneous power P_i(t), and a hierarchy of entanglement metrics (concurrence, BEE, TMI, QFI, ABEE). They find that the instantaneous power peak occurs before strong quantum correlations form, implying coherent transport dominates peak power; entanglement and scrambling emerge later. Under fair charging, increasing interaction order or participation number alone does not guarantee higher power; fully collective interactions provide genuine advantages, while partial extensions can suppress power due to competing correlations. The results clarify when quantum correlations are responsible for improvements and have implications for designing efficient quantum energy storage.

Abstract

Identifying the physical origin of enhanced charging performance in many-body quantum batteries is a key challenge in quantum thermodynamics. We investigate whether improvements in stored energy and instantaneous charging power arise from genuine quantum correlations or from coherent collective dynamics that are not intrinsically quantum. We compare the time evolution of energetic quantities with a hierarchy of information-theoretic measures probing bipartite, tripartite, and further-partite correlations. Across different battery charger configurations, we find a consistent temporal ordering in which the instantaneous power peaks before the buildup of strong quantum correlations, indicating that peak charging is dominated by coherent transport, while entanglement and scrambling develop at later times. Furthermore, charging protocols based on k local interactions are examined under both unconstrained and norm-constrained (fair) settings, enabling a clear distinction between classical scaling effects and genuine collective enhancements. Increasing the interaction order or the participation number does not automatically translate into higher charging power. Instead, the performance is primarily dictated by how many particles actually become mutually correlated and contribute to entanglement. Fully collective interactions provide a genuine advantage because all particles participate coherently, whereas partially extended interaction schemes fail to monotonically increase the number of effectively interacting particles, and therefore do not guarantee improved charging efficiency.

Figures (7)

• Figure 1: Noninteracting battery charged by an interacting Hamiltonian.Bipartite entanglement $(a_1,b_1,c_1)$: Time evolution of the instantaneous power $P_i$, concurrence between the first and last spins $C(1,N)$, and bipartite entanglement entropy (BEE) $S_{N/2}$. Tripartite entanglement $(a_2,b_2,c_2)$: Time evolution of $P_i$ and tripartite mutual information (TMI) $I_3$. Multipartite entanglement $(a_3,b_3,c_3)$: Time evolution of $P_i$, quantum Fisher information (QFI) $F_Q$, and average entanglement entropy (AEE) $\overline{S}_{N/2}$. Panels correspond to: $(a_1, a_2, a_3)$$J_x = 1$, $J_y = J_z = 0$; $(b_1, b_2, b_3)$$J_x = J_y = 1$, $J_z = 0$; $(c_1, c_2, c_3)$$J_x = J_y = J_z = 1$. Number of spins: $N = 8$ and $h_x=h_z=1$.
• Figure 2: Interacting battery charged by an noninteracting Hamiltonian.Bipartite entanglement $(a_1,b_1,c_1)$: Time evolution of the instantaneous power $P_i$, concurrence between the first and last spins $C(1,N)$, and bipartite entanglement entropy (BEE) $S_{N/2}$. Tripartite entanglement $(a_2,b_2,c_2)$: Time evolution of $P_i$ and tripartite mutual information (TMI) $I_3$. Multipartite entanglement $(a_3,b_3,c_3)$: Time evolution of $P_i$, quantum Fisher information (QFI) $F_Q$, and average entanglement entropy (AEE) $\overline{S}_{N/2}$. Panels correspond to: $(a_1, a_2, a_3)$$J_x = 1$, $J_y = J_z = 0$; $(b_1, b_2, b_3)$$J_x = J_y = 1$, $J_z = 0$; $(c_1, c_2, c_3)$$J_x = J_y = J_z = 1$. Number of spins: $N = 8$ and $h_x=h_z=1$.
• Figure 3: Unfair charging. (a) Parallel charging: Time evolution of the stored energy $\Delta E$ for a noninteracting battery, where each spin is charged independently by a local transverse field of strength $h_x=1$ and $h_x=N$ (with all spin-spin interactions set to zero). (b) Global charging: Time evolution of the stored energy $\Delta E$ for the same noninteracting battery, charged by an all-to-all interacting spin charger with interaction strengths $J_x=1$ and $J_x=N$, in the absence of any external transverse field. $N=8$ (open boundary conditions), with $h_z=1$ fixing the battery energy scale.
• Figure 4: Fair charging with $\boldsymbol{h_x \neq 0}$ and $\boldsymbol{J_x = h_x}$. Instantaneous power $P_i$ as a function of time $t$ for a noninteracting battery with $h_z = 1$, charged by a $\kappa$-local interacting charger in the presence of an additional transverse field of strength $h_x$. The charger Hamiltonian is normalized such that $\lVert \hat{H}_C \rVert = N (=8)$ by tuning the parameters $J_x$ and $h_x$ under the constraint $J_x = h_x$. The system size is $N = 8$.
• Figure 5: Fair charging with $\boldsymbol{h_x \neq 0}$ and $\boldsymbol{J_x > h_x}$. A noninteracting battery with $h_z = 1$ is charged by a $\kappa = 1,2,3$-local interacting charger in the presence of an additional transverse field of strength $h_x$. The charger Hamiltonian is normalized such that $\lVert \hat{H}_C \rVert = N (=8)$ by tuning the parameters under the constraint $J_x > h_x$. Panels (a) and (b) show, respectively, the instantaneous power $P_i$ and the ABEE $\overline{S}$ as functions of time $t$.