non-Hermitian Model Research Articles

Solvable non-Hermitian skin effects and real-space exceptional points: non-Hermitian generalized Bloch theorem

Non-Hermitian systems can exhibit extraordinary boundary behaviors, known as the non-Hermitian skin effects, where all the eigenstates are localized exponentially at one side of lattice model. To give a full understanding and control of non-Hermitian skin effects, we have developed the non-Hermitian generalized Bloch theorem to provide the analytical expression for all solvable eigenvalues and eigenstates, in which translation symmetry is broken due to the open boundary condition. By introducing the Vieta’s theorem for any polynomial equation with arbitrary degree, our approach is widely applicable for one-dimensional non-Hermitian tight-binding models. With the non-Hermitian generalized Bloch theorem, we can analyze the condition of existence or non-existence of the non-Hermitian skin effects at a mathematically rigorous level. Additionally, the non-Hermitian generalized Bloch theorem allows us to explore the real-space exceptional points. We also establish the connection between our approach and the generalized Brillouin zone method. To illustrate our main results, we examine two concrete examples including the Su–Schrieffer–Heeger chain model with long-range couplings, and the ladder model with non-reciprocal interaction. Our non-Hermitian generalized Bloch theorem provides an efficient way to analytically study various non-Hermitian phenomena in more general cases.

Dynamical localization transition in the non-Hermitian lattice gauge theory

Local constraint in the lattice gauge theory provides an exotic mechanism that facilitates the disorder-free localization. However, the understanding of nonequilibrium dynamics in the non-Hermitian lattice gauge model remains limited. Here, we investigate the quench dynamics in a system of spinless fermions with nonreciprocal hopping in the Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb{Z}}}_{2}$$\\end{document} gauge field. By employing a duality mapping, we systematically explore the non-Hermitian skin effect, localization-delocalization transition, and real-complex transition. Through the identification of diverse scaling behaviors of quantum mutual information for fermions and spins, we propose that the non-Hermitian quantum disentangled liquids exist both in the localized and delocalized phases, the former originates from the Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb{Z}}}_{2}$$\\end{document} gauge field and the latter arises from the non-Hermitian skin effect. Furthermore, we demonstrate that the nonreciprocal dissipation causes the flow of quantum information. Our results provide valuable insights into the nonequilibrium dynamics in the gauge field, and may be experimentally validated using quantum simulators.

Transfer learning from Hermitian to non-Hermitian quantum many-body physics

Identifying phase boundaries of interacting systems is one of the key steps to understanding quantum many-body models. The development of various numerical and analytical methods has allowed exploring the phase diagrams of many Hermitian interacting systems. However, numerical challenges and scarcity of analytical solutions hinder obtaining phase boundaries in non-Hermitian many-body models. Recent machine learning methods have emerged as a potential strategy to learn phase boundaries from various observables without having access to the full many-body wavefunction. Here, we show that a machine learning methodology trained solely on Hermitian correlation functions allows identifying phase boundaries of non-Hermitian interacting models. These results demonstrate that Hermitian machine learning algorithms can be redeployed to non-Hermitian models without requiring further training to reveal non-Hermitian phase diagrams. Our findings establish transfer learning as a versatile strategy to leverage Hermitian physics to machine learning non-Hermitian phenomena.

Non-hermiticity in spintronics: oscillation death in coupled spintronic nano-oscillators through emerging exceptional points

The emergence of exceptional points (EPs) in the parameter space of a non-hermitian (2D) eigenvalue problem has long been interest in mathematical physics, however, only in the last decade entered the scope of experiments. In coupled systems, EPs give rise to unique physical phenomena, and enable the development of highly sensitive sensors. Here, we demonstrate at room temperature the emergence of EPs in coupled spintronic nanoscale oscillators and exploit the system’s non-hermiticity. We observe amplitude death of self-oscillations and other complex dynamics, and develop a linearized non-hermitian model of the coupled spintronic system, which describes the main experimental features. The room temperature operation, and CMOS compatibility of our spintronic nanoscale oscillators means that they are ready to be employed in a variety of applications, such as field, current or rotation sensors, radiofrequeny and wireless devices, and in dedicated neuromorphic computing hardware. Furthermore, their unique and versatile properties, notably their large nonlinear behavior, open up unprecedented perspectives in experiments as well as in theory on the physics of exceptional points expanding to strongly nonlinear systems.

Nonlinear Landau-Zener-Stückelberg-Majorana problem with non-Hermitian models

Nonlinear Landau-Zener-Stückelberg-Majorana problem with non-Hermitian models

Breakdown of the Meissner effect at the zero exceptional point in non-Hermitian two-band BCS model

The spontaneous symmetry breaking of a continuous symmetry in complex field theory at the exceptional point (EP) of the parameter space is known to exhibit interesting phenomena, such as the breakdown of a Higgs mechanism. In this work, we derive the complex Ginzburg–Landau model from a non-Hermitian two-band Bardeen–Cooper–Schrieffer model via path integral and investigate its spontaneous symmetry breaking. We find that analog to the Higgs mechanism, the Meissner effect of the complex Ginzburg–Landau model also breaks down at the EP while the gap parameters stay finite.

Emergent non-Hermitian models

Emergent non-Hermitian models

Entanglement entropy and topological properties in a long-range non-Hermitian Su–Schrieffer–Heeger model

We employ entanglement entropy to investigate the topological properties of the extended long-range non-Hermitian Su–Schrieffer–Heeger (SSH) model. We show how long-range hopping, nearest-neighbor hopping, and the non-Hermitian term influence the entanglement entropy in the SSH model, which serves as a valuable tool for examining the topological features of the SSH model. Our research reveals a remarkable phenomenon: entanglement entropy exhibits singular behavior in specific regions that precisely align with the spatial locations of topological phase transitions in the extended long-range SSH model. These findings are further supported by the application of winding numbers and energy spectra, offering comprehensive evidence for the topological aspects of both Hermitian and non-Hermitian SSH models. As a result, the singularity in entanglement entropy provides a robust framework for characterizing topological phase transitions.

Nonlinear topological laser on the non-Hermitian Haldane model with higher-order corner states.

The non-Hermitian skin effect (NHSE) on the non-Hermitian Haldane model with gain and loss on the honeycomb lattice with the outline of a triangle is discussed. The NHSE only occurs on the edge of the lattice, transforming the edge modes into the higher-order corner modes. The NHSE can also occur on a lattice with only loss, which can be treated as a lattice with gain and loss as well as a global loss added to it. When the saturated gain is added to the three corner sites of the dissipative lattice, a single-mode laser system is obtained. When any one site is stimulated initially, the system will reach a saturated state depending on the distribution of the corner modes, and the stable laser light is emitted by sites at the corners.

Instantaneous dynamics and localization near exceptional point in breathing solitons

We report the instantaneous dynamics of breathing soliton near exceptional point (EP) and propose the nonlinear non-Hermitian coupling model in gain nonlinearity systems. In such nonlinear systems, the mode intensity change is weakened by gain nonlinearity, and the relative phase displays localization in probability distribution. Moreover, such localization can be enhanced by EPs, which is helpful for EP sensing. Experiments and simulations are carried out in breathing soliton lasers. We find that the instantaneous breathing frequency and the relative phase are time-varying near EP. Meanwhile, the distribution of the relative phase displays localization as the theoretical prediction. These results not only are important to the nonlinear science but also can help to understand the EP properties, especially for the application of breathing soliton systems for EP sensing.

The Topological Phase Transitions near the Exceptional Point of a Non-Hermitian Electromagnetic Lattice Model

In this paper, we take the double-layer three-component non-Hermitian Lieb lattice system as an example to discuss the topological properties of the non-Hermitian lattice point electromagnetic field system. The topological phase transitions of the Lieb lattice system near the exceptional point are analyzed by calculating the topological invariants. We find that there are abundant topological phase transitions near the exceptional point. This study will help us explore more topological physical phenomena of electromagnetic fields of lattice systems in condensed-matter physics.

Proposal for Observing Yang-Lee Criticality in Rydberg Atomic Arrays.

Yang-Lee edge singularities (YLES) are the edges of the partition function zeros of an interacting spin model in the space of complex control parameters. They play an important role in understanding non-Hermitian phase transitions in many-body physics, as well as characterizing the corresponding nonunitary criticality. Even though such partition function zeroes have been measured in dynamical experiments where time acts as the imaginary control field, experimentally demonstrating such YLES criticality with a physical imaginary field has remained elusive due to the difficulty of physically realizing non-Hermitian many-body models. We provide a protocol for observing the YLES by detecting kinked dynamical magnetization responses due to broken PT symmetry, thus enabling the physical probing of nonunitary phase transitions in nonequilibrium settings. In particular, scaling analyses based on our nonunitary time evolution circuit with matrix product states accurately recover the exponents uniquely associated with the corresponding nonunitary CFT. We provide an explicit proposal for observing YLES criticality in Floquet quenched Rydberg atomic arrays with laser-induced loss, which paves the way towards a universal platform for simulating non-Hermitian many-body dynamical phenomena.

Non-Hermitian Haldane-Hubbard model: Effective description of one- and two-body dissipation

Non-Hermitian Haldane-Hubbard model: Effective description of one- and two-body dissipation

Correlations at higher-order exceptional points in non-Hermitian models

Correlations at higher-order exceptional points in non-Hermitian models

Superscattering emerging from the physics of bound states in the continuum

We study the Mie-like scattering from an open subwavelength resonator made of a high-index dielectric material, when its parameters are tuned to the regime of interfering resonances. We uncover a novel mechanism of superscattering, closely linked to strong coupling of the resonant modes and described by the physics of bound states in the continuum (BICs). We demonstrate that the enhanced scattering occurs due to constructive interference described by the Friedrich-Wintgen mechanism of interfering resonances, allowing to push the scattering cross section of a multipole resonance beyond the currently established limit. We develop a general non-Hermitian model to describe interfering resonances of the quasi-normal modes, and study subwavelength dielectric nonspherical resonators exhibiting avoided crossing resonances associated with quasi-BIC states. We confirm our theoretical findings by a scattering experiment conducted in the microwave frequency range. Our results reveal a new strategy to boost scattering from non-Hermitian systems, suggesting important implications for metadevices.

Localization and topological transitions in generalized non-Hermitian SSH models

We study the localization and topological transitions of the generalized non-Hermitian SSH models. Under the open boundary condition, two delocalization transitions are found due to the competition between the Anderson localization and the boundary localization from the nontrivial edge states and the non-Hermitian skin effect. Under the periodic boundary condition, only one delocalization transition is found due to the disappearance of the non-Hermitian skin effect. The winding numbers of energy and the Lyapunov exponents in analytical form are obtained to exactly characterize the two delocalization transitions. It finds that the delocalization transitions don't accompany the topological transition. Furthermore, the large on-site non-Hermiticity is detrimental to the topological transitions, delocalization and localization transitions. However, the large nonreciprocal hopping enhances the Anderson localizations but is detrimental to the delocalization transition. The above analyses are verified by calculating the energy gap and the inverse of the participation ratio numerically.

Lock-in phenomena in non-Hermitian coupled systems

Coupled-mode theory has been widely employed in various branches of photonics, such as nano-photonics and non-Hermitian optics. Here we show that it can also be used as an effective physical model for clarifying various optical mode lock-in phenomena, which have been revealed to essentially originate from non-Hermitian degeneracies. We discuss the lock-in effects in physical systems through prototypical examples of optical feedback self-injection frequency lock-in technology and lock-in phenomena of ring laser gyroscopes (RLGs). Seemingly unrelated effects have been unified through one general non-Hermitian mode coupling model. Furthermore, based on our theoretical framework, we have uncovered the underlying mechanism of lock-in in RLGs and analyzed how this effect can be systematically suppressed or even eliminated

General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents

We establish a general mapping from one-dimensional non-Hermitian mosaic models to their non-mosaic counterparts. This mapping can give rise to mobility edges and even Lyapunov exponents in the mosaic models if critical points of localization or Lyapunov exponents of localized states in the corresponding non-mosaic models have already been analytically solved. To demonstrate the validity of this mapping, we apply it to two non-Hermitian localization models: an Aubry–André-like model with nonreciprocal hopping and complex quasiperiodic potentials, and the Ganeshan–Pixley–Das Sarma model with nonreciprocal hopping. We successfully obtain the mobility edges and Lyapunov exponents in their mosaic models. This general mapping may catalyze further studies on mobility edges, Lyapunov exponents, and other significant quantities pertaining to localization in non-Hermitian mosaic models.

Complex fixed points of the non-Hermitian Kondo model in a Luttinger liquid

Complex fixed points of the non-Hermitian Kondo model in a Luttinger liquid

Coexistence of stable and unstable population dynamics in a nonlinear non-Hermitian mechanical dimer.

Non-Hermitian two-site dimers serve as minimal models in which to explore the interplay of gain and loss in dynamical systems. In this paper, we experimentally and theoretically investigate the dynamics of non-Hermitian dimer models with nonreciprocal hoppings between the two sites. We investigate two types of non-Hermitian couplings; one is when asymmetric hoppings are externally introduced, and the other is when the nonreciprocal hoppings depend on the population imbalance between the two sites, thus introducing the non-Hermiticity in a dynamical manner. We engineer the models in our synthetic mechanical setup comprised of two classical harmonic oscillators coupled by measurement-based feedback. For fixed nonreciprocal hoppings, we observe that, when the strength of these hoppings is increased, there is an expected transition from a PT-symmetric regime, where oscillations in the population are stable and bounded, to a PT-broken regime, where the oscillations are unstable and the population grows/decays exponentially. However, when the non-Hermiticity is dynamically introduced, we also find a third intermediate regime in which these two behaviors coexist, meaning that we can tune from stable to unstable population dynamics by simply changing the initial phase difference between the two sites. As we explain, this behavior can be understood by theoretically exploring the emergent fixed points of a related dimer model in which the nonreciprocal hoppings depend on the normalized population imbalance. Our study opens the way for the future exploration of non-Hermitian dynamics and exotic lattice models in synthetic mechanical networks.