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arXiv:2603.17557

Imaginary Gauge Field and Non-Hermitian Topological Transition Emerging Through Attenuation-Gauge Duality in Conservative Systems

Haoran Nie, Chaoran Jiang, Xiangying Shen, Lei Xu

cond-mat.otherquant-phSubmitted Mar 18, 2026• Announced Mar 19, 2026
arXivHTMLPDF

Abstract

Non-Hermitian physics traditionally relies on active gain--loss modulation or non-reciprocal couplings, which often introduce significant complexity, compromise stability, and offer very limited scalability in conservative systems. Here we propose an attenuation-gauge duality paradigm in which non-Hermitian topology emerges within fully passive, conservative systems through coupling to a structured reservoir. We derive that a spatially varying reservoir can establish an attenuation-gauge duality, where the spatial variation manifests as an emergent imaginary gauge field in the effective dynamics. It drives the boundary accumulation of skin modes while preserving energy conservation, analogous to Feshbach projection in quantum open systems. We validate this universal wave paradigm via macroscopic mechanical metamaterials, demonstrating that the direction of the skin effect can be reversed by tuning a single passive coupling parameter$t_\perp$, driven by a topological phase transition characterized by the spectral winding number. This framework also allows for a nonlinear extension, where amplitude-dependent coupling can induce intrinsic topological transitions.

Comments
6 pages, 3 figures

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Non-Hermitian physics traditionally relies on active gain--loss modulation or non-reciprocal couplings, which often introduce significant complexity, compromise stability, and offer very limited scalability in conservative systems. Here we propose an attenuation-gauge duality paradigm in which non-Hermitian topology emerges within fully passive, conservative systems through coupling to a structured reservoir. We derive that a spatially varying reservoir can establish an attenuation-gauge duality, where the spatial variation manifests as an emergent imaginary gauge field in the effective dynamics. It drives the boundary accumulation of skin modes while preserving energy conservation, analogous to Feshbach projection in quantum open systems. We validate this universal wave paradigm via macroscopic mechanical metamaterials, demonstrating that the direction of the skin effect can be reversed by tuning a single passive coupling parametert⊥t_\perpt⊥​, driven by a topological phase transition characterized by the spectral winding number. This framework also allows for a nonlinear extension, where amplitude-dependent coupling can induce intrinsic topological transitions.
The non-Hermitian skin effect is one of the most remarkable topological features of non-conservative physics. It causes a macroscopic accumulation of states at the boundaries of a confined system, opening new ways for controlling and directing waves in non-Hermitian settings. This effect has recently been observed in experiments with Bose-Einstein condensates of exciton polaritons and ultracold bosonic quantum gases. The underlying physics is captured by a mean-field Hamiltonian with a trapping potential and an imaginary gauge field. While prior work has examined the effect of the imaginary gauge field term on the condensate itself, its effect on the collective excitations on top of the condensate remained unexplored. Here, we develop a new theory for the Bogoliubov excitations in a non-Hermitian framework and systematically study their spectrum across different interaction regimes. By analysing the position expectation values, we find that while the repulsive interactions oppose the localisation of the condensate due to the skin effect, the excitations remain strongly affected by the imaginary gauge field. As a consequence, in the presence of harmonic confinement, we predict a strong shift in the dipole oscillation frequency, which can be observed in experiments. This is in contrast to Hermitian systems, where this frequency is fixed by the trap dimensions. Furthermore, we develop a consistent second-quantised field theory of the collective excitations in this non-Hermitian system. Strikingly, we find that a second-quantised treatment removes the shift of the dipole oscillation frequency entirely. This intriguing discrepancy between the two theoretical approaches to the treatment of elementary excitations in a non-Hermitian system can be resolved in experiments.
The non-Hermitian skin effect (NHSE) -- the anomalous boundary accumulation of an extensive number of bulk modes -- has emerged as a hallmark of non-Hermitian physics, with broad implications for transport, sensing, and topological classification. A central open question is how magnetic or synthetic gauge fields influence this boundary phenomenon. Here, we develop a theoretical framework for magnetic control of the NHSE along line boundaries in two-dimensional single-band lattices. Using a non-Hermitian extension of the anisotropic Harper--Hofstadter model as a representative example, we show that magnetic fields suppress the geometric skin effect in reciprocal models, whereas skin localization can persist in nonreciprocal systems. The analysis disentangles the interplay of flux, nonreciprocity, and boundary geometry, revealing that magnetic fields mitigate or suppress the NHSE through distinct physical mechanisms -- such as bulk localization via Landau or Anderson physics, or the restoration of effective reciprocity. In particular, the geometry-dependent skin effect in reciprocal systems is found to be fragile against even weak magnetic fields.
In all known schemes for the non-Hermitian skin effect, the non-Hermitian ingredient that drives the skin localization, whether asymmetric hopping or gain and loss, is invariably introduced by hand as an independent model parameter along the skin direction. Here we show that when two spatial coordinates do not commute, the skin effect can break free of this paradigm: a gain-loss potential applied along one coordinate automatically generates non-reciprocity along the other through the coordinate noncommutativity, driving all eigenstates to pile up exponentially at a boundary. We term this phenomenon the noncommutative skin effect. The inverse skin length is proportional to the noncommutativity parameter and is given by an analytic formula, exact in the thermodynamic limit and verified by exact diagonalization of lattice models; the reflection symmetry of the imaginary potential furnishes an exact criterion for the presence or absence of the effect, valid rigorously for finite-size systems. For a sinusoidal imaginary potential, the skin direction of all eigenstates flips collectively at parameter points fixed purely by geometry. Because the flip point is independent of the potential strength, the reversal constitutes a zero-crossing measurement scheme intrinsically robust against systematic errors, from which the noncommutativity parameter can be extracted directly. The qualitative transition of the eigenstates from uniform to exponentially localized renders the effect a nonperturbative probe of spatial noncommutativity, and the Peierls-phase structure of its lattice model is in principle accessible to cold-atom synthetic dimensions, photonic resonators, and topolectrical circuits.
We propose a general framework, termed the imaginary gauge phase imprint (IGPI), which enables engineering arbitrarily configurable wavefunctions with exact solutions and self-organization dynamics in any-dimensional non-Hermitian lattices under imaginary gauge fields. Using this method, we uncover a novel phase with exact critical wavefunctions, dubbed the skin critical phase (SCP), which is marked by unconventional localization, topological-skin, and dynamical characteristics. Furthermore, we validate the IGPI by imprinting and visualizing complex fractal states with Sierpinski-carpet and Koch-snowflake profiles, as well as exotic super-moire and 3D-moire states in regular lattices. Our work not only offers fresh insights into non-Hermitian critical and fractal physics, but also provides a rigorous paradigm for controlling and visualizing wavefunction patterns using the IGPI in engineered non-Hermitian systems.
Fractionalization in ideal Chern bands and non-Hermitian topological physics are two active but so far separate research directions. Merging these, we generalize the notion of ideal Chern bands to the non-Hermitian realm and uncover several striking consequences both on the level of band theory and in the strongly interacting regime. Specifically, we show that the lowest band of a Kapit--Mueller lattice model with an imaginary gauge potential satisfies a generalized ideal condition with complex Berry curvature in sync with a complex quantum metric. The ideal band remains purely real and exactly flat on both the torus and cylinder: eigenstates are extended on the torus, while on the cylinder all right and left eigenstates localize at the boundaries, yielding a non-Hermitian skin effect without spectral winding. In the interacting regime, we find that the generalized ideal condition stabilizes an incompressible liquid at fractional fillings, retaining intrinsic non-Hermitian features on both cylinder and torus, while strikingly distinct on different manifolds. On the cylinder, the ground states are always skin-Laughlin states. In contrast, on the torus, we instead observe an unconventional competition between topologically ordered Laughlin-like states and negative collective modes, arising purely from non-Hermiticity.
Conventional Chern insulators rely on breaking time-reversal symmetry via magnetic fields or synthetic gauge fields. Here we introduce a fundamentally different paradigm: a static lattice without any gauge field becomes a Chern insulator solely through the cooperation of two non-Hermitian ingredients: on-site loss and non-reciprocal coupling. Neither effect alone suffices; only their synergy opens a topological gap and gives rise to robust chiral edge states with a nonzero Chern number. The underlying mechanism originates from a non-Hermitian chiral molecule formed by the lossy sites, whose dynamically dominant mode carries an orbital angular momentum that effectively generates a synthetic flux after the fast-decaying degrees of freedom are eliminated. Our results establish non-Hermitian cooperation as a versatile resource for inducing Chern topology without external fields or temporal modulations, opening a new route to topological phases in open classical and quantum systems.