Quantum Scars Hold the Key to Persistent Work

Author: Denis Avetisyan

New research reveals that quantum many-body scars can retain significantly more extractable work than typical quantum systems, offering a potential path toward more efficient quantum energy storage.

A dynamical quantum protocol, realized in blockaded Rydberg atom arrays, leverages coherent rotations-specifically, $RY(\theta) = e^{-i\frac{\theta}{2}Y}$-and qubit resets to inject energy into the PXP Hamiltonian, creating highly excited states that, upon relaxation, yield a steady-state subsystem possessing extensive energy extractable via unitary operations, demonstrating a pathway for controlled energy management at the quantum level.

This study investigates the relationship between entanglement entropy and ergotropy in scarred quantum systems, specifically the PXP model, demonstrating enhanced work extraction capabilities compared to thermal states.

While quantum systems typically evolve towards thermal equilibrium and lose the capacity to perform work, certain non-ergodic states defy this expectation. This work, titled ‘Ergotropy of quantum many-body scars’, investigates the surprising ability of quantum many-body scars to retain extractable energy, quantified by their ergotropy. We demonstrate a direct relationship between ergotropy and entanglement in the PXP model, revealing that scarred states possess significantly higher energy storage potential than their thermal counterparts. Could these findings pave the way for engineering efficient quantum batteries based on the principles of non-ergodic quantum dynamics?

The Illusion of Thermal Equilibrium

The Eigenstate Thermalization Hypothesis (ETH) proposes a surprising resolution to the question of how isolated quantum systems – those with no external interactions – can seemingly evolve towards thermal equilibrium. Counterintuitively, this isn’t achieved through traditional dissipation or energy loss, but rather through the properties of the system’s individual energy eigenstates. The ETH asserts that these eigenstates themselves statistically resemble thermal distributions, meaning each eigenstate encodes the same information about long-time averages as would be predicted by thermal physics. In essence, the system doesn’t need to interact with an environment to appear thermal; the thermal behavior is already ‘built in’ to the structure of its quantum states. This implies that even though quantum mechanics is fundamentally deterministic, described by the $Schrödinger$ equation, observing a thermalized system is not a failure of quantum mechanics, but a consequence of the statistical properties of complex quantum states. The implications extend to understanding the foundations of statistical mechanics and offer a path toward predicting the behavior of many-body quantum systems without needing to solve their time evolution.

The assertion that isolated quantum systems ultimately succumb to thermal equilibrium presents a profound conceptual challenge. Quantum mechanics, at its core, is a deterministic theory; given the initial state of a system, its future evolution is, in principle, precisely predictable through the Schrödinger equation. Thermalization, however, implies a loss of information about this initial state – the system ‘forgets’ its beginnings and settles into a state characterized only by a few macroscopic parameters like temperature. This apparent contradiction arises because thermalization isn’t a process of information destruction, but rather its effective scrambling into an enormous number of degrees of freedom. The initial information isn’t lost to the universe, but becomes practically inaccessible, encoded in complex correlations between particles. Consequently, while the underlying quantum evolution remains deterministic, predicting the system’s behavior becomes equivalent to predicting a random variable, mirroring the statistical nature of thermodynamics. This delicate interplay between deterministic dynamics and emergent statistical behavior is central to understanding how the quantum world gives rise to the classical world we experience.

The pursuit of quantum technologies and the discovery of emergent material properties hinge on a detailed comprehension of when and how quantum systems stray from perfect thermalization. While the Eigenstate Thermalization Hypothesis provides a valuable framework, deviations from this predicted behavior aren’t simply noise-they represent opportunities. These anomalies can signal the presence of many-body localization, where interactions prevent energy distribution and preserve quantum coherence, or hint at the existence of exotic phases of matter with unconventional order. Investigating these deviations requires precise control and measurement of quantum systems, allowing researchers to harness the preserved quantum information for computation or to engineer materials with tailored properties, potentially leading to breakthroughs in areas ranging from quantum simulation to superconductivity and beyond. Understanding these limits, therefore, is not about finding flaws in established theory, but about charting a path toward realizing the full potential of quantum mechanics.

Scars in the Quantum Landscape

Quantum many-body scars are a recently discovered phenomenon challenging the conventional understanding of thermalization in isolated quantum systems. Typically, interacting quantum systems evolve towards thermal equilibrium, characterized by a loss of memory of the initial state and eigenstates that appear random. However, scarred systems exhibit a specific set of eigenstates – the scars – that retain a degree of coherence and memory, resisting this thermalization process. These non-thermal eigenstates are characterized by a spatial localization, similar to eigenstates in non-interacting systems, and their presence is sustained even with strong interactions. This persistence of non-thermal behavior distinguishes scarred systems and opens the possibility of manipulating quantum information within a seemingly thermalizing environment, as the scars provide protected states resistant to decoherence.

Quantum many-body scars present a deviation from the typical thermalization expected in closed quantum systems, offering potential advantages for quantum information tasks. Traditional thermalization leads to the loss of initial state information and limits the duration of quantum coherence. However, the non-thermal eigenstates associated with these scars retain memory of the initial state, potentially enabling longer coherence times and more robust storage of quantum information. This persistence of information could facilitate the development of novel quantum memory architectures and computational paradigms that circumvent the limitations imposed by decoherence and thermal noise. The ability to initialize and retrieve information from these scar states without significant degradation is a key feature currently under investigation for practical quantum applications.

Quantum many-body scars exhibit a notable ability to perform work on the external environment, a characteristic that deviates from the behavior of thermalized systems. This work extraction capacity is quantified by Ergotropy, which measures the maximum useful work obtainable from a quantum state. In systems displaying scars, Ergotropy scales extensively with system size – meaning it increases proportionally to the volume of the system – indicating a significant potential for work extraction. This is in direct contrast to thermal states, where Ergotropy scales only sub-extensively, limited by the system’s surface area, and therefore represents a fundamentally different energetic behavior. The extensive scaling of Ergotropy in scar states suggests these non-thermal eigenstates retain a degree of coherence and non-randomness that allows for sustained work extraction, unlike the randomized energy distribution of a fully thermalized state.

Probing the Limits of Equilibrium

The PXP model, a spin-1/2 chain with periodic boundary conditions defined by the Hamiltonian $H = J \sum_{i=1}^N (\sigma_z^i \sigma_z^{i+1} + \sigma_x^i \sigma_x^{i+1})$, serves as a prominent platform for investigating quantum many-body scars. These non-equilibrium states, characterized by atypical persistence during time evolution following a quantum quench, are readily observable in the PXP model due to its constrained dynamics and the resulting localization of excitations. Specifically, the model’s integrability leads to the formation of exact eigenstates that exhibit extended spatial correlations, facilitating the identification and analysis of scarred states through measurements of quantities like entanglement entropy and local observables. The simplicity of the PXP Hamiltonian allows for both analytical and numerical investigations, enabling researchers to characterize the properties of these scars, including their energy spectrum, spatial extent, and robustness to perturbations.

The Forward Scattering Approximation (FSA) is utilized to analyze the algebraic properties of quantum many-body scars within non-Hermitian models. This technique focuses on identifying and characterizing the eigenstates associated with these scars by examining the scattering of an initial state across the Hilbert space. Specifically, FSA allows researchers to determine the effective Hamiltonian governing the scarred subspace, revealing its eigenvalue spectrum and corresponding decay rates. By analyzing these parameters, the dynamics of the scarred states can be understood, including their robustness against perturbations and their contribution to long-lived oscillations in the system’s evolution. The method relies on identifying a set of “sticking” states that resist typical thermalization, and characterizing the interactions between these states to map out the algebraic structure of the scar manifold.

Rydberg Atom Arrays are utilized as a programmable quantum simulator to experimentally realize and investigate the PXP model and associated quantum scars. These arrays leverage the strong, long-range interactions between highly excited Rydberg states of neutral atoms, allowing for precise control over the system’s Hamiltonian. By manipulating laser fields, researchers can engineer the desired interactions and create a controllable environment for observing the dynamics of quantum many-body scars. Experimental measurements, such as time-of-flight imaging and fluorescence detection, are used to probe the system’s state and verify theoretical predictions regarding the formation, stability, and propagation of these scars, offering a crucial validation of the theoretical framework and providing insights into non-equilibrium dynamics in isolated quantum systems.

The Ghost in the Machine: Entanglement and Information

Quantum systems exhibit correlations beyond those described by classical physics, and entanglement entropy serves as a fundamental tool to quantify these connections. This measure doesn’t simply count linked particles; it assesses the degree to which a subsystem is quantumly connected to the rest of the system – a connection vital for understanding the peculiar behavior of quantum scars. These scars, representing non-thermal eigenstates, defy typical expectations by retaining memory of initial conditions, and their existence is intrinsically linked to a unique entanglement structure. Specifically, scar states demonstrate a suppressed growth of entanglement entropy compared to the expected volume law seen in thermal states, suggesting a limited sharing of quantum information. Therefore, detailed analysis of entanglement entropy provides crucial insights into the formation, stability, and properties of these quantum scars, ultimately revealing a deeper understanding of how quantum information shapes the dynamics of isolated many-body systems.

Characterizing entanglement within many-body systems requires moving beyond simple measures, and researchers utilize refined tools like Von Neumann Entropy, Quantum Fisher Information, and Mutual Information to dissect the complex correlations present. These calculations reveal distinct behaviors between different quantum states: scar states, arising from non-thermal dynamics, surprisingly exhibit a sub-volume law for entanglement entropy-meaning entanglement growth is suppressed compared to systems at thermal equilibrium. Conversely, thermal states, representing the expected behavior of closed quantum systems, adhere to a volume law, where entanglement scales directly with the system’s size. This difference in scaling is not merely a mathematical curiosity; it provides a crucial signature for identifying and understanding the unique properties of quantum scar states and their deviation from typical thermalization processes, offering insights into the system’s underlying dynamics and potential for preserving quantum information.

The connection between a system’s entanglement and its underlying physical Hamiltonian, as proposed by the Haldane Conjecture, provides a powerful lens through which to examine the emergence of quantum scars and their impact on system behavior. Recent investigations have revealed a quantifiable relationship between the bound energy, denoted as $Q$, and the von Neumann entropy, $S_{vN}$, demonstrating that $Q$ scales proportionally to the square of $S_{vN}$. This finding suggests that the energy associated with these stable, non-thermal states is directly linked to the degree of quantum correlations present within the system, offering a pathway to predict and potentially control the formation of quantum scars by manipulating entanglement properties. Understanding this proportionality is crucial for developing a more complete picture of how these unusual states arise and influence the dynamics of complex quantum systems.

Beyond Equilibrium: Implications and Future Directions

The longstanding expectation in physics was that isolated quantum systems, when disturbed, would rapidly evolve toward a state of thermal equilibrium, losing all memory of their initial conditions. However, the recent discovery of quantum many-body scars fundamentally challenges this notion. These scars are non-thermal states that persist during the time evolution of a quantum system, behaving as stable, localized excitations amidst otherwise chaotic dynamics. This persistence isn’t simply a matter of energy conservation; rather, these states exhibit an unusual resilience to decoherence and thermalization, hinting at a breakdown of the conventional ergodic hypothesis. Consequently, the existence of quantum many-body scars is not merely a curiosity, but a potentially transformative discovery for quantum information processing. These states could serve as robust storage locations for quantum information, offering a pathway toward building more stable and reliable quantum computers, and potentially enabling novel quantum technologies that circumvent the limitations imposed by decoherence.

The intentional creation of quantum many-body scars, once considered rare exceptions, is now becoming increasingly feasible through sophisticated experimental techniques like quantum quenches and coherent rotation. Quantum quenches, involving the rapid alteration of a system’s parameters, can ‘freeze’ specific quantum states, preventing the expected descent into thermal equilibrium and nurturing the formation of these non-thermal scars. Complementarily, coherent rotation – the precise manipulation of a quantum system using external fields – allows researchers to sculpt and refine these scars, enhancing their stability and controllability. This ability to engineer these unique states isn’t merely an academic curiosity; it’s a crucial step toward harnessing quantum systems for practical applications, potentially leading to novel forms of quantum memory, enhanced quantum computation, and the development of entirely new quantum technologies that circumvent the limitations of traditional thermal systems.

The exploration of quantum many-body scars echoes historical thought experiments like Maxwell’s Demon, prompting a re-evaluation of the relationship between information and energy. Recent research delves into the limits of extractable work, quantified by a property called Ergotropy, to better understand how these non-thermal states defy the typical progression toward equilibrium. Notably, investigations into systems where the system length, $L$, is four times the number of constituents, $N$, have demonstrated a surprising robustness – energy remains conserved throughout time evolution. This conservation isn’t merely a restatement of established physics; it suggests that these scarred states represent a fundamentally different way information and energy interact, potentially offering pathways to sustain coherence and perform computation without succumbing to the usual constraints of thermalization and entropy increase.

The pursuit of quantum many-body scars feels less like discovering fundamental physics and more like meticulously cataloging elegant failure modes. This paper, detailing the connection between entanglement and ergotropy, highlights how these scars can retain extractable work-a tantalizing prospect for quantum batteries. It’s a neat trick, maintaining higher ergotropy than thermal states, but the history of technology is littered with systems that looked promising on paper. As John Bell once observed, ‘No phenomenon is a genuine mystery until it has been explained.’ This research doesn’t solve the mystery of efficient energy storage, it simply refines the parameters of the problem. The bug tracker is, inevitably, preparing for another entry. They don’t deploy – they let go.

What’s Next?

The demonstration of sustained ergotropy within these scarred many-body systems is… predictable, really. One builds a carefully constrained system, and is surprised it doesn’t immediately succumb to entropy? It’s a comforting narrative. The real question, of course, isn’t if these scars can hold onto extractable work, but how quickly the inevitable approximations and imperfections of actual hardware will bleed that advantage away. They’ll call it ‘decoherence mitigation’ and raise funding, naturally.

The connection to ‘quantum batteries’ feels… optimistic. The current iteration likely requires more bespoke control than is realistically achievable, and the energy densities are probably still abysmal. One suspects the scaling will be unkind. Nevertheless, the exploration of non-thermal states for work extraction is valuable, if only to map out the limitations with excruciating detail. It used to be a simple bash script, controlling a few qubits. Now it’s a cascading series of error-correcting codes and calibration routines.

Future work will undoubtedly focus on robustness – shielding these fragile scars from the relentless onslaught of the real world. Perhaps investigating the interplay between different types of scars, or finding ways to engineer them into systems with more practical parameters. The documentation lied again, of course, about the stability of the initial state. It always does. But the pursuit of controlled non-equilibrium states will continue, because, at the end of the day, tech debt is just emotional debt with commits.

Original article: https://arxiv.org/pdf/2512.19801.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/