Charging power enhancement at the phase transition of a non-integrable quantum battery

Abstract

Exploiting many-body interaction and critical phenomena to improve the performance of quantum batteries is an emerging and promising line of research. A central question in this direction is whether quantum phase transitions can enhance the charging energy or the power. While preliminary works have addressed this problem in fine-tuned integrable models, its characterization in non-integrable systems remains limited due to the demanding numerical requirements. Here, we investigate a one-dimensional Axial Next-Nearest-Neighbor Ising model as an example of non-integrable quantum battery charged via a quantum-quench protocol. In contrast to integrable cases, we find that criticality in this setting can lead to a pronounced enhancement of the charging power. Our findings inform quantum-battery design of many-qubit systems and are amenable to experimental verification on current quantum-simulation platforms, including neutral-atom arrays.

Figures (6)

• Figure 1: (a) Phase diagram of the ANNNI model in the $(\kappa,h)$ plane, adapted from Ref. cea2024exploring ($J_1=1$). The cyan dashed line is the exactly-solvable Peschel-Emery (PE) line. It partially overlap with the gray line representing the Ising phase transition (I). We also report the Kosterlitz-Thouless (blue line) and Pokrovsky-Talapov (red line) phase transitions (KT and PT respectively). (b) Cartoon view of a QB charging protocol based on a double quantum quench of length $\tau$. Here, $|\psi(t) \rangle$ is the state of the QB at a given time $t$, $H_{0}$ indicates both the initial and the final Hamiltonian and $H_{1}$ the one used during the quench. The initial state $\ket{\psi(0)}$ is taken as the ground state of $H_0$.
• Figure 2: (a) Injected energy per spin as a function of the charging time $\tau$. We consider $J_1=1$, $h=0.4$ for both $H_0$ and $H_1$ (open boundary conditions), plotting results for three different values of the frustration parameter $\kappa$ (see legend) and taking $\kappa'=\kappa+0.1$. We report results for a chain length $L=16$. (b) Same as in (a) but for the charging power.
• Figure 3: (a) Maximum charging power per spin for a 16-spin chain with open boundary conditions, as a function of the frustration parameter $\kappa$ (with $\kappa'=\kappa+0.1$). The other parameters are set as $J_1=1$, $h=0.4$ for both $H_0$ and $H_1$. By increasing $\kappa$ we cross the following phase transitions: Ising (gray), Kosterlitz-Thouless (blue), and Pokrovsky-Talapov (red). Points are calculated from exact diagonalization and interpolated via the black curve. (b) Same as in (a) but for $h=0.2$.
• Figure 4: (a) Maximum charging power per spin for a 16-spin chain with open boundary conditions, as a function of the frustration parameter $\kappa$ ($\kappa'=\kappa+0.1$). The other parameters are set as $J_1=1$, $h=1.2$ for both $H_0$ and $H_1$. (b) Same as in (a) but for $h=1$. (c) Same as in (a) but for $h=0.8$. We have the following phase transitions for increasing $\kappa$: Ising (gray), Kosterlitz-Thouless (blue), and Pokrovsky-Talapov (red). We also report the region associated to the exactly-solvable Peschel-Emery (cyan) line. Points are calculated from exact diagonalization and interpolated via the black curve.
• Figure 5: (a)Maximum charging power per spin for a 16-spin chain with open boundary conditions, as a function of the field $h$and at fixed $\kappa=0$. Both $H_0$ (characterized by the transverse field $h$) and $H_1$ (characterized by the transverse field $h'=h+0.1$) realize the integrable Transverse Field Ising (TFI) model and no evident signature is present at the transition. Points are calculated from exact diagonalization and interpolated via the black curve. (b) Same as in (a) but taking $h=h'$, $\kappa=0$ and $\kappa'=0.1$. Here, $H_1$ realizes the non-integrable ANNNI model and the maximum power stabilizes at the Ising transition of $H_0$.