In a groundbreaking study that promises to reshape our understanding of quantum behavior, physicists at the University of Michigan have uncovered new fundamental principles regarding the nature of semi-localized quantum states in materials. Led by Professor Kai Sun, a theorist known for his rigorous analytical approach, the research reveals that power-law “skin” modes—exotic quantum states exhibiting algebraic decay—are not rare curiosities that require fine-tuned conditions. Instead, these states emerge robustly in systems with two or more spatial dimensions, overturning long-standing assumptions about their fragility and enabling promising new avenues for quantum technologies.
Historically, physicists have categorized the ways quantum waves or particles occupy materials into two distinct types: localized modes, where energy remains confined to a small region due to barriers or defects, and propagating waves, which travel freely across the material. The localized modes exhibit rapid exponential decay, meaning their influence vanishes quickly outside a limited zone, while propagating waves show no decay at all and carry energy across long distances. Between these two extremes, theorists postulated the existence of intermediate states exhibiting a slower algebraic, or power-law, decay, but these were thought to be rare phenomena requiring delicate tuning.
The new research challenges this narrative by demonstrating that power-law skin modes—formerly regarded as esoteric exceptions—are in fact abundantly realized when moving beyond traditional one-dimensional models into the richer, more complex terrain of two or higher-dimensional systems. By expanding the conceptual framework, Sun and his collaborators showed that these modes naturally arise along the boundaries or “skin” of materials in a robust manner, unaffected by minor perturbations or imperfections that would typically suppress such states.
From a mathematical perspective, the distinction between exponential and power-law decay lies in the rate at which the amplitude of the quantum state diminishes with distance. Exponential decay plummets sharply, often making localized states highly sensitive to environmental noise or structural variations. Power-law decay, while slower, still restricts energy spread but does so in a way that effectively balances confinement with extended reach. This subtle but profound difference implies that information or energy can propagate partially across the system while retaining localized features, a property with direct implications for next-generation devices.
One of the most striking findings in the study is the critical role of a material’s geometry—specifically its aspect ratio—in shaping the behavior of these power-law skin modes. Unlike previous models that treated boundaries as uniform or one-dimensional edges, the team’s exploration of two-dimensional shapes revealed that the spatial configuration dramatically influences mode distribution and decay patterns. Such sensitivity to shape paves the way for engineered materials where quantum states can be precisely tailored by geometry alone, without resorting to cumbersome fine-tuning of material parameters or external fields.
The discovery stands to impact quantum computing fundamentally. Quantum bits, or qubits, which can exist in complex superpositions of states, require delicate management of coherence and information flow. The newfound robustness of power-law modes suggests qubits may simultaneously host strongly localized modes for stable computation and power-law modes that transmit quantum information efficiently across a device. This duality could overcome some of the intractable challenges faced by present-day quantum architectures, offering a fresh design paradigm inspired directly by these newly elucidated physical principles.
Professor Sun describes the research as an exciting confluence of foundational physics and practical opportunity. “This work reveals novel concepts on the fundamental side, while also opening new opportunities for future applications,” he stated. Unlike many breakthroughs rooted in abstract theory but distant from implementation, the firm mathematical footing and experimental relevance of these modes make them immediately compelling for exploration in quantum materials, photonics, and beyond.
Underlying this advance is a reconsideration of the “non-Hermitian skin effect,” a counterintuitive phenomenon where certain open quantum systems exhibit an accumulation of states along material edges, defying the traditional bulk-boundary correspondence. The new algebraic approach generalizes this effect across arbitrary dimensions and connects it to a broadened Fermi surface formula—a pivotal tool in quantum theory that relates the geometry of electron states to their physical properties. Sun and colleagues’ method provides a unifying framework that bridges previously disparate observations and theoretical models.
At its core, the research exemplifies how expanding dimensionality in quantum models can unlock behaviors impossible to capture in simpler, one-dimensional analogies. The familiar rubber-band analogy, often used to illustrate localized versus traveling waves, falls short when confronted with higher-dimensional lattice structures and complex boundary conditions. By accounting for these richer geometries, the team unveiled a landscape where power-law decays are not only widespread but also definitional of the system’s fundamental physics.
Overcoming traditional limitations, the study also underscores computational and experimental feasibility. Because the discovered power-law modes are extremely robust and do not require fine-tuning, they are more likely to be observed and manipulated in real laboratory settings. This robustness contrasts sharply with delicate quantum states that collapse under minor environmental disturbances, thus raising hopes for practical realization in solid-state platforms or photonic simulators.
Looking ahead, the implications extend far beyond academic curiosity. Quantum materials exploiting algebraic non-Hermitian skin effects could usher in new classes of devices leveraging semi-localized states for enhanced control of light, sound, or electronic signals. Precision shaping of device geometry could tailor performance characteristics, offering a versatile toolkit for engineers and physicists alike.
The study, published in the prestigious journal Physical Review X, was partly funded by the Office of Naval Research, highlighting the strategic interest in exploring fundamental quantum phenomena with potential defense and technological applications. Key contributors besides Professor Sun include research fellow Kai Zhang and graduate student Chang Shu, whose efforts helped deepen and extend the theoretical framework.
Ultimately, this remarkable investigation opens a new frontier in quantum physics by demonstrating that once-elusive power-law skin modes are both universal and tunable features of materials in higher dimensions. By blending mathematical sophistication with visionary physical insight, the research redefines what quantum systems can do and sets the stage for innovations that harness the subtle interplay between localization, propagation, and geometry at the quantum frontier.
Subject of Research: Quantum semi-localized states and power-law skin modes in higher-dimensional non-Hermitian systems
Article Title: Algebraic Non-Hermitian Skin Effect and Generalized Fermi Surface Formula in Arbitrary Dimensions
News Publication Date: 11-Aug-2025
Web References: 10.1103/cwwd-bclc
Image Credits: Credit: K. Zhang et al. Phys. Rev. X. 2025 (DOI: 10.1103/cwwd-bclc) Used under a CC-BY license.
Keywords
quantum mechanics, non-Hermitian physics, power-law decay, localization, quantum computing, skin effect, algebraic modes, higher dimensions, quantum materials, boundary phenomena, Fermi surface, quantum technologies
