Quantum Many-Body Battery

• The paper reveals that quantum many-body scars enable extensive ergotropy by allowing significant work extraction from high-energy nonthermal eigenstates.
• It employs the PXP model in Rydberg atom chains to demonstrate coherent charging, persistent revivals, and effective energy redistribution.
• Implications include designing quantum energy storage systems that exploit ergodicity-breaking to achieve robust and scalable work extraction.

A quantum many-body battery is a many-body quantum system, typically modeled by lattice spin or Rydberg-atom arrays, capable of storing and delivering extractable energy (ergotropy) in a way fundamentally enabled or optimized by the existence of quantum many-body scars (QMBS). These scars are special nonthermal eigenstates that weakly break ergodicity, allowing unusually high extractable work even at high energy densities—contrary to the equilibrium expectation that high-energy eigenstates are passive. The notion of a quantum many-body battery thus provides a physical and operational bridge between ergodicity-breaking phenomena and energy storage/extraction protocols in quantum simulators (Zhi et al., 22 Dec 2025).

1. Quantum Many-Body Scars and Their Role in Ergotropy

Quantum many-body scars are a vanishingly small subset of eigenstates in an otherwise thermalizing, nonintegrable many-body spectrum. Scarred eigenstates are characterized by:

• Atypical (subthermal) entanglement entropy, despite high energy density.
• Large overlap with simple product (e.g., Néel or CDW) states.
• Weak violation of the Eigenstate Thermalization Hypothesis (ETH): time evolution from certain initial states exhibits persistent revivals and memory retention beyond what is possible in thermal eigenstates.
• Ability to sustain persistent nonthermal expectation values of local observables for long times (Turner et al., 2017, Zhi et al., 22 Dec 2025).

These properties underlie their utility for energy storage: scarred eigenstates support extensive ergotropy, i.e., a scaling of extractable work with subsystem size, exceeding what is attainable in thermal states of equivalent energy density (Zhi et al., 22 Dec 2025).

2. Ergotropy: Definition and Analytical Structure

Ergotropy is defined as the maximal extractable work from a quantum state $\rho_A$ of a subsystem $A$ with Hamiltonian $H_A$, via unitary (coherent) operations: $$W_\mathrm{erg}(\rho_A) = \operatorname{Tr}[\rho_A H_A] - E_\mathrm{passive}$$ where $E_\mathrm{passive}$ is the energy of the passive state (eigenvalues of $\rho_A$ rearranged in descending order mapped to ascending energy eigenvalues). Passive states are those from which no work can be extracted unitarily. Scarred eigenstates, despite being highly excited, exhibit non-passive reduced density matrices with extensive ergotropy, in contrast to thermal eigenstates whose reduced states are nearly passive with $W_\mathrm{erg} \sim 0$ (Zhi et al., 22 Dec 2025).

3. Scar States in the PXP Model: A Paradigmatic Quantum Many-Body Battery

The PXP model, realized in Rydberg atom chains, encapsulates the many-body battery mechanism: $H_\mathrm{PXP} = \sum_{i=1}^L P_{i-1} X_i P_{i+1}$ where $P_i$ projects onto the absence of excitation at site $i$ (Rydberg blockade constraint), and $X_i$ is the Pauli-$x$ operator. The model supports a near-harmonic “scar tower” of nonthermal eigenstates at $E \approx 0$.

By preparing an initial product state, such as the $\mathbb{Z}_2$ Néel state $|1\,0\,1\,0\,\cdots\rangle$, and subjecting it to a global uniform coherent rotation,

$U(\theta) = \exp(-i \theta \sum_i Y_i/2),$

(where $Y_i$ is Pauli $y$), energy is coherently injected into the system and redistributed across the chain in a manner conditioned by scar dynamics.

Upon bipartitioning into subsystem $A$ and environment $\bar{A}$, the reduced density matrix $\rho_A$ for scarred initial states retains substantial ergotropy: $W_\mathrm{erg}\sim L_A$ for subsystem size $L_A$, whereas in the thermal regime ($\theta \sim \pi/2$), $W_\mathrm{erg}$ vanishes in the thermodynamic limit (Zhi et al., 22 Dec 2025).

The ergotropy and entanglement entropy $S_\mathrm{vN}$ of these reduced states exhibit a robust, model-independent phenomenological relation: $$Q = E - W_\mathrm{erg} \propto \frac{S^2_\mathrm{vN}}{n + m L}$$ with $n, m$ constants dependent on the mixture of scar and thermal features. This characterizes the interplay: maximal extractable work requires low quantum entropy—scarred dynamics uniquely enables this at high energies.

4. Dynamical Charging and Readout Protocols

The quantum many-body battery is operated via a coherent “charging” protocol:

• Initialization: System is reset to a product state (usually the $\mathbb{Z}_2$ state).
• Coherent charging: A global pulse $U(\theta)$ injects energy by controllably mixing in components of the scar tower.
• Thermalization window: The system evolves unitarily for a time sufficient for dephasing, leading to a quasistationary entangled state with nonzero ergotropy.
• Work extraction: The maximal work is extracted via an optimal unitary on subsystem $A$ (passive state rearrangement).

For the PXP model, the extracted work density $W_\mathrm{erg}/L$ is maximized near $\theta=0$ (pure scar regime) and vanishes near $\theta=\pi/2$ (thermal regime), providing continuous control of battery charge through pulse angle (Zhi et al., 22 Dec 2025).

5. Experimental Feasibility and Platforms

Rydberg atom arrays currently fulfill all physical requirements to realize quantum many-body batteries. Key features include:

• Realization of the PXP Hamiltonian with long coherence times ($\tau\sim 50\!\!-\!\!100\,\mu\mathrm{s}$).
• Global single-qubit rotations for charging protocol.
• Observation of scar-induced revivals and extensive ergotropy in atom chains of $L\sim50$–$100$.
• Compatibility with mid-circuit measurement and reloading, enabling repeated charge/discharge cycles (Zhi et al., 22 Dec 2025).

Other platforms such as superconducting qubit arrays or trapped ions implementing scarred Hamiltonians may be equally suitable.

6. Broader Significance, Outlook, and Generalizations

The demonstration that QMBS can endow a generic thermal system with significant, controllable ergotropy highlights a new physical mechanism for quantum energy storage. Unlike conventional batteries reliant on extensive ground-state degeneracy or low-lying excitations, quantum many-body batteries exploit ergodicity-breaking at high energy density for robust, scalable storage and extraction of work through quantum coherences.

This paradigm sets criteria for designing and identifying systems—such as those with strong kinetic constraints, nonintegrable but ETH-violating spectra, and accessible scar subspaces—that maximize work storage. The anti-correlation between quantum entropy and ergotropy links quantum information properties (entanglement) to operational performance in quantum thermodynamics.

Applications are anticipated in quantum device architectures requiring nonthermal state stabilization, rapid energy injection and extraction, and persistent coherence at high energies. Ongoing research includes the extension of this concept to Floquet (periodically driven) systems, open/dissipative setups, and platforms beyond Rydberg arrays, as well as optimizing control for work extraction protocols (Zhi et al., 22 Dec 2025).

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Key Reference Table

Concept/Protocol	Model/Platform	Scar Feature for Battery	arXiv Reference
Scar-enabled ergotropy & storage	PXP/Rydberg chain	Extensive W_erg, revivals	(Zhi et al., 22 Dec 2025)
Quantum scar properties and ETH	PXP, general scars	Weak ETH violation	(Turner et al., 2017, Serbyn et al., 2020)
Experimental realization	Rydberg arrays	Battery protocol feasible	(Zhi et al., 22 Dec 2025)

For detailed construction, performance metrics, and connection to general nonequilibrium dynamics in QMBS systems, see (Zhi et al., 22 Dec 2025) and cited works.