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arXiv:2605.10637

Dynamical Criticality Behind Energy-Storage Singularities in Quantum Batteries

Zheng Liu, Wen-Hui Nie, Yi-jia Yang, Lin-Cheng Wang, Chang-shui Yu

quant-phSubmitted May 11, 2026• Announced May 12, 2026• 0 citations• Revised May 12, 2026 (v2)

v1 · May 11, 2026 v2 · May 12, 2026 v3 · Oct 3, 2026

Abstract

Energy-storage singularities in quantum batteries are often associated with equilibrium quantum criticality. Here we show that, in quench-driven many-body batteries, such singularities can originate from dynamical criticality in momentum space. Using the transverse-field Ising chain as a representative free-fermion quantum battery, we develop a momentum-resolved description of the charging process. The long-time stored energy forms a dephasing plateau whose dependence on the quench strength becomes nonanalytic when a real dynamical critical momentum emerges. More generally, for free-fermion two-band quantum batteries, each momentum sector acts as an independent coherent charging channel, and the condition for a dynamical quantum phase transition (DQPT) is equivalent to perfect normalized charging of the critical mode. At the critical times, this mode has a vanishing Loschmidt amplitude, maximal normalized stored energy, and zero instantaneous power at the turning point between energy absorption and backflow. We further show that the single-mode charging signal-to-noise ratio (SNR) develops sharp signatures at the same critical times, providing a direct charging-based probe of DQPT. Thus, nonequilibrium criticality does not simply enhance the total stored energy or power, which remain shaped by noncritical modes, but reorganizes energy storage by selecting optimal microscopic charging channels. Our results establish a mode-resolved connection between DQPT and quantum-battery charging, suggesting a route toward controlling many-body energy storage through dynamical criticality.

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Energy-storage singularities in quantum batteries are often associated with equilibrium quantum criticality. Here we show that, in quench-driven many-body batteries, such singularities can originate from dynamical criticality in momentum space. Using the transverse-field Ising chain as a representative free-fermion quantum battery, we develop a momentum-resolved description of the charging process. The long-time stored energy forms a dephasing plateau whose dependence on the quench strength becomes nonanalytic when a real dynamical critical momentum emerges. More generally, for free-fermion two-band quantum batteries, each momentum sector acts as an independent coherent charging channel, and the condition for a dynamical quantum phase transition (DQPT) is equivalent to perfect normalized charging of the critical mode. At the critical times, this mode has a vanishing Loschmidt amplitude, maximal normalized stored energy, and zero instantaneous power at the turning point between energy absorption and backflow. We further show that the single-mode charging signal-to-noise ratio (SNR) develops sharp signatures at the same critical times, providing a direct charging-based probe of DQPT. Thus, nonequilibrium criticality does not simply enhance the total stored energy or power, which remain shaped by noncritical modes, but reorganizes energy storage by selecting optimal microscopic charging channels. Our results establish a mode-resolved connection between DQPT and quantum-battery charging, suggesting a route toward controlling many-body energy storage through dynamical criticality.

We investigate the charging dynamics and energy storage performance of a quantum battery defined by an anisotropic spin-1/2 XY chain, extended by the inclusion of anisotropic three-spin interactions. This system possesses a rich ground-state phase diagram featuring non-trivial gapped topological phases separated by quantum critical lines. Utilizing the fermionization technique, we exactly diagonalize the Hamiltonian and analyze the charging process through a quantum quench from an initial state to a final Hamiltonian configuration. We derive an analytical expression for the upper bound of the stored energy. Significantly, we find that the steady-state stored energy is consistently equal to one-half of the corresponding theoretical maximum throughout the parameter regime investigated. Furthermore, we provide analytical approximations for the charging peak and demonstrate that the underlying topological phase transitions leave distinct and detectable signatures in the charging landscape. These results establish a framework for understanding the interplay between ground-state topology, quantum criticality, and nonequilibrium energy-storage dynamics in quantum spin-chain batteries.

Phase transitions (PTs) in quantum many-body systems offer a powerful route to manipulate the performance of quantum batteries (QBs). Here, we investigate an anisotropic Dicke QB with Kerr nonlinearity, focusing on the role of PTs in the charging process of the QB system. By analyzing how the Kerr nonlinearity reshapes the cavity level-spacing structure, we find that multiple near-degeneracies emerge at specific nonlinearity strengths. Away from the region of multiple near-degeneracies, the stable stored energy is governed primarily by the ergodic-nonergodic transition (ENET), whereas within this region it is controlled by first- and second-order dissipative phase transitions (DPTs). We employ Liouvillian spectral theory to quantify the critical slowing down associated with the DPTs, and use the Wigner function to characterize the properties of the cavity field in the vicinity of criticality. We optimize the charging process via reinforcement learning (RL) and reveal the physical mechanism underlying performance enhancement from the perspective of ergodic and nonergodic phase dynamics. Our results offer a feasible pathway for manipulating and optimizing quantum battery performance based on intrinsic PT behaviors.

We investigate the performance of a one-dimensional dimerized XY chain as a spin quantum battery. Such integrable model shows a rich quantum phase diagram that emerges through a mapping of the spins onto auxiliary fermionic degrees of freedom. We consider a charging protocol relying on the double quench of an internal parameter, namely the strength of the dimerization, and address the energy stored in the systems. We observe three distinct regimes, depending on the timescale characterizing the duration of the charging: a short-time regime related to the dynamics of the single dimers, a long-time regime related to the recurrence time of the system at finite size, and a thermodynamic limit time regime. In the latter, the energy stored is almost unaffected by the charging time and the precise values of the charging parameters, provided the quench crosses a quantum phase transition. Finally, we analytically prove that the three-timescale behavior and the strong dependence of the energy stored on the quantum phase diagram also hold in the quantum Ising chain in a transverse field. Our results can play a relevant role in the design of stable solid-state quantum batteries.

Abstract Starting from the observation that the reduced state of a system strongly coupled to a bath is, in general, an athermal state, we introduce and study a cyclic battery–charger quantum device that is in thermal equilibrium, or in a ground state, during the charge storing stage. The cycle has four stages: the equilibrium storage stage is interrupted by disconnecting the battery from the charger, then work is extracted from the battery, and then the battery is reconnected with the charger; finally, the system is brought back to equilibrium. At no point during the cycle are the battery–charger correlations artificially erased. We study the case where the battery and charger together comprise a spin-1/2 Ising chain, and show that the main characteristics—the extracted energy and the thermodynamic efficiency—can be enhanced by operating the cycle close to the quantum phase transition point. When the battery is just a single spin, we find that the output work and efficiency show a scaling behavior at criticality and derive the corresponding critical exponents. Due to always present correlations between the battery and the charger, operations that are equivalent from the perspective of the battery can entail different energetic costs for switching the battery–charger coupling. This happens only when the coupling term does not commute with the battery’s bare Hamiltonian, and we use this purely quantum leverage to further optimize the performance of the device.

Quantum batteries are quantum systems designed to store energy and release it on demand. The optimization of their performance is an intensively studied topic within the realm of quantum technologies. Such optimization forces the question: how do quantum many-body systems work as quantum batteries? To address this issue, we rely on symmetry and symmetry breaking via quantum phase transitions. Specifically, we analyze a dimerized quantum XY chain in a transverse field as a prototype of an energy storage device. This model, which is characterized by ground states with different symmetries depending on the Hamiltonian parameters, can be mapped onto a spinless fermionic chain with superconducting correlations, displaying a rich quantum phase diagram. We show that the stored energy strongly depends on the quantum phase diagram of the model when large charging times are considered.

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.