non-Hermitian Skin Effect Research Articles

Anomalous non-Hermitian dynamical phenomenon on the quantum circuit

The anomalous non-Hermitian dynamical phenomenon with the non-Hermitian skin effect (NHSE) attracts wide attention due to its novel physics and promising applications. Here, we propose a new type of non-unitary discrete-time quantum walk system demonstrating the NHSE and anomalous non-Hermitian dynamical phenomena, including the dynamical chiral phenomenon, the funneling phenomenon on the domain wall, and the anomalous reflection on the phase impurity. Furthermore, we design the quantum circuit experiments of these quantum walk systems and numerically simulate them with quantum noises to verify the robustness of the non-Hermitian dynamical phenomenon on the noisy intermediate-scale quantum (NISQ) devices. Our work paves the way for implementing the non-Hermitian dynamical phenomenon on the quantum circuit.

Non-Hermitian skin effect in a one-dimensional interacting Bose gas

Non-Hermitian skin effect in a one-dimensional interacting Bose gas

Mixed state behavior of Hermitian and non-Hermitian topological models with extended couplings

Geometric phase is an important tool to define the topology of the Hermitian and non-Hermitian systems. Besides, the range of coupling plays an important role in realizing higher topological indices and transition among them. With a motivation to understand the geometric phases for mixed states, we discuss finite temperature analysis of Hermitian and non-Hermitian topological models with extended range of couplings. To understand the geometric phases for the mixed states, we use Uhlmann phase and discuss the merit-limitation with respect extended range couplings. We extend the finite temperature analysis to non-Hermitian models and define topological invariant for different ranges of coupling. We include the non-Hermitian skin effect, and provide the derivation of topological invariant in the generalized Brillouin zone and their mixed state behavior also. We also adopt mixed geometric phases through interferometric approach, and discuss the geometric phases of extended-range (Hermitian and non-Hermitian) models at finite temperature.

Non-Hermitian edge burst without skin localization

In a class of non-Hermitian quantum walk in lossy lattices with open boundary conditions, an unexpected peak in the distribution of the decay probabilities appears at the edge, dubbed edge burst. It is proposed that the edge burst is originated jointly from the non-Hermitian skin effect (NHSE) and the imaginary gaplessness of the spectrum [Wen-Tan Xue et al., Phys. Rev. Lett. 128, 120401 (2022)]. Using a particular one-dimensional lossy lattice with a nonuniform loss rate, we show that the edge burst can occur even in the absence of skin localization. Furthermore, we discuss that the edge burst may not appear if the spectrum satisfies the imaginary gaplesness condition. Aside from its fundamental importance, by removing the restrictions on observing the edge burst effect, our results open the door to broader design space for future applications of the edge burst effect.

Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect

Recent years have seen remarkable development in open quantum systems effectively described by non-Hermitian Hamiltonians. A unique feature of non-Hermitian topological systems is the skin effect, anomalous localization of an extensive number of eigenstates driven by nonreciprocal dissipation. Despite its significance for non-Hermitian topological phases, the relevance of the skin effect to quantum entanglement and critical phenomena has remained unclear. Here, we find that the skin effect induces a nonequilibrium quantum phase transition in the entanglement dynamics. We show that the skin effect gives rise to a macroscopic flow of particles and suppresses the entanglement propagation and thermalization, leading to the area law of the entanglement entropy in the nonequilibrium steady state. Moreover, we reveal an entanglement phase transition induced by the competition between the unitary dynamics and the skin effect even without disorder or interactions. This entanglement phase transition accompanies nonequilibrium quantum criticality characterized by a nonunitary conformal field theory whose effective central charge is extremely sensitive to the boundary conditions. We also demonstrate that it originates from an exceptional point of the non-Hermitian Hamiltonian and the concomitant scale invariance of the skin modes localized according to the power law. Furthermore, we show that the skin effect leads to the purification and the reduction of von Neumann entropy even in Markovian open quantum systems described by the Lindblad master equation. Our work opens a way to control the entanglement growth and establishes a fundamental understanding of phase transitions and critical phenomena in open quantum systems far from thermal equilibrium.

Manipulating the non-Hermitian skin effect in optical ring resonators

Non-Hermitian skin effects (NHSEs) enrich the traditional band theories and give rise to unique non-Hermitian topological properties. Here, we reveal a different type of NHSE, termed the V-shaped NHSE, and explore an on-chip optical ring resonator platform to demonstrate the NHSE in telecommunication wavelength. By tuning the hopping and loss modulation, we work out a phase diagram that reveals the phase transition of the NHSE. Besides the conventional NHSE and the frequency-dependent bipolar NHSE, another type of NHSE is observed featuring an interesting V shape in its special skin states distribution. We further design a silicon ring resonator array with loss-assisted antiresonating coupling as the link resonators to demonstrate the nontrivial NHSE. The simulations show that one can tune the number of states piled up at different ends by switching the NHSE from conventional, bipolar to V-shaped types continuously. Our work enriches the NHSE phase transitions and implies potential in on-chip light modulation by the NHSE.

Nonreciprocal Su-Schrieffer-Heeger lattice in the presence of next-nearest-neighboring coupling

We pay attention to the band structure of the nonreciprocal Su-Schrieffer-Heeger (SSH) lattice modified by next-nearest-neighboring (NNN) coupling. It is found that the NNN coupling induces the chiral symmetry by breaking the particle-hole symmetry, leading to the energies of the end modes in the topologically-nontrivial region dependent on the structural parameters. Also, with the increase of NNN coupling, the encounter of the bulk bands modifies the phase transition manner in a new way. The other phenomenon lies in that the localization of the end modes and the non-Hermitian skin effect can be modulated efficiently by the interplay between the NNN and nonreciprocal couplings. Based on these results, one can understand the nontrivial role of NNN coupling in modifying the energy bands and topological properties of the nonreciprocal SSH lattice.

Multiple phase transitions and anomalous non-Hermitian skin effect

Non-Hermiticity is revolutionizing the common understanding in the Hermitian scope by interfacing with topological physics. A single non-Hermitian band can host nontrivial topology that is defined over the nonzero windings of the system's eigenvalues, but not the eigenvectors, as opposed to the Hermitian topological systems. This unique non-Hermitian band topology is responsible for the intriguing non-Hermitian skin effect. Here, we show that the band topology of non-Hermitian one-band models can experience multiple phase transitions. Each transition is identified by a change of the eigenvalue winding. Such an interesting phenomenon is enabled by strategically manipulating the long-range couplings. Associated with the multiple phase transitions, the non-Hermitian skin effect exhibits anomalous behaviors, i.e., in different phases, the skin modes take on different forms of wave localizations. At the transition points, the skin modes evolve into Bloch-wavelike extended states, as if the Hermiticity is restored. For demonstration, we consider a modified Hatano-Nelson model with nonreciprocal next-nearest neighbor couplings. Therein, two phase transitions are identified, corresponding to a stationary and a dynamic one (with respect to the reciprocal nearest-neighbor coupling). Exact analytical derivations are performed to analyze the phase transitions and the associated anomalous non-Hermitian skin effect, which show consistency with the numerical results based on the generalized Brillouin zone method. Our work reveals rich non-Hermitian topological physics in one-band systems, which are considered to be topologically trivial in Hermitian systems. By further showing the anomalous non-Hermitian skin effect, intriguing wave manipulations may inspire experiments in classical realms such as photonics and phononics where versatile non-Hermitian controls are feasible.

Anatomy of open-boundary bulk in multiband non-Hermitian systems

Although the non-Bloch band theory is a milestone in elaborating bulk energy bands of non-Hermitian systems under the open-boundary condition (OBC), vital issues related to multivalued functions of non-Hermitian energy bands remain unsolved. In this paper, we anatomize the bulk properties of one-dimensional multiband non-Hermitian systems under OBC. We put forward the energy-band branches (EBBs) to settle the multivalued functions of non-Hermitian energy bands, which become gapped or gapless corresponding to disconnected or connected EBBs in the complex energy plane, where the branch points and branch cuts play a crucial role. We clarify the precise significance of the non-Hermitian skin effect, which illustrates the asymptotic behavior of EBB eigenstates (bulk eigenstates) in the deep bulk and compensates previous non-Bloch band theory. We also obtain a general expression of open-boundary Green's functions based on such EBBs and generalized Brillouin zones, useful for studies on non-Hermitian dynamical evolution.

Continuum of Bound States in a Non-Hermitian Model.

In a Hermitian system, bound states must have quantized energies, whereas free states can form a continuum. We demonstrate how this principle fails for non-Hermitian systems, by analyzing non-Hermitian continuous Hamiltonians with an imaginary momentum and Landau-type vector potential. The eigenstates, which we call "continuum Landau modes" (CLMs), have Gaussian spatial envelopes and form a continuum filling the complex energy plane. We present experimentally realizable 1D and 2D lattice models that host CLMs; the lattice eigenstates are localized and have other features matching the continuous model. One of these lattices can serve as a rainbow trap, whereby the response to an excitation is concentrated at a position proportional to the frequency. Another lattice can act a wave funnel, concentrating an input excitation onto a boundary over a wide frequency bandwidth. Unlike recent funneling schemes based on the non-Hermitian skin effect, this requires a simple lattice design with reciprocal couplings.

Topological Spin Excitations in Non-Hermitian Spin Chains with a Generalized Kernel Polynomial Algorithm.

Spectral functions of non-Hermitian Hamiltonians can reveal the existence of topologically nontrivial line gaps and the associated topological edge modes. However, the computation of spectral functions in a non-Hermitian many-body system remains an open challenge. Here, we put forward a numerical approach to compute spectral functions of a non-Hermitian many-body Hamiltonian based on the kernel polynomial method and the matrix-product state formalism. We show that the local spectral functions computed with our algorithm reveal topological spin excitations in a non-Hermitian spin model, faithfully reflecting the nontrivial line gap topology in a many-body model. We further show that the algorithm works in the presence of the non-Hermitian skin effect. Our method offers an efficient way to compute local spectral functions in non-Hermitian many-body systems with tensor networks, allowing us to characterize line gap topology in non-Hermitian quantum many-body models.

Topological semimetal phase and dynamical characterization in a non-Hermitian two-leg ladder model

We show the phase transition between the trivial and the topological semimetal phases in a non-Hermitian two-leg ladder model. We find that, the topological properties of this special model can be captured by a equivalent model with chiral symmetry in which the equivalent model owns the pure imaginary nonreciprocal intercell and long-range hopping simultaneously. Based on the equivalent model, we reveal that the system possesses the gapless topological semimetal phase induced by four exceptional points, which is different from the general topological semimetal phase usually owning two exceptional points. Significantly, we demonstrate that the system has the distinct transmission behaviors within the trivial and topological semimetal phases, leading the phase transition between trivial and topological semimetal phases and the boundary between left and right non-Hermitian skin effects can both be characterized dynamically via the propagation speed of the evolved initial state. Our investigation further supplies the contents on a topological semismetal phase in the non-Hermitian two-leg ladder model and may provide a possible tool to visualize the phase transition of the topological semimetal phase.

Characterizing and tuning exceptional points using Newton polygons

The study of non-Hermitian degeneracies—called exceptional points (EPs)—has become an exciting frontier at the crossroads of optics, photonics, acoustics, and quantum physics. Here, we introduce the Newton polygon method as a general algebraic framework for characterizing and tuning EPs. Newton polygons, first described by Isaac Newton, are conventionally used in algebraic geometry, with deep roots in various topics in modern mathematics. We propose and illustrate how the Newton polygon method can enable the prediction of higher-order EPs, using a recently experimentally realized optical system. Using the paradigmatic Hatano-Nelson model, we demonstrate how our method can predict the presence of the non-Hermitian skin effect. As further application of our framework, we show the presence of tunable EPs of various orders in PT-symmetric one-dimensional models. We further extend our method to study EPs in higher number of variables and demonstrate that it can reveal rich anisotropic behaviour around such degeneracies. Our work provides an analytic recipe to understand exceptional physics.

Electrical circuit realization of topological switching for the non-Hermitian skin effect

Non-Hermitian systems reveal rich physics beyond the Hermitian regime, and have aroused great interest. One remarkable physical phenomenon is the non-Hermitian skin effect. Recently, topological switching for the non-Hermitian skin effect has been theoretically proposed in cold-atom systems. However, experimental realization of such a phenomenon remains a great challenge. Here, we theoretically propose and experimentally demonstrate a topological switch for the non-Hermitian skin effect in electrical circuit networks. By controlling the operational amplifier and other electric components, the nonreciprocal transport of probability for electrical signals is observed when the switch is turned on. Furthermore, the robustness of such a topological switch is demonstrated both theoretically and experimentally when perturbations are added. Our study provides an avenue for controlling electrical signals in circuit networks, with potential applications in the field of integrated circuit design.

Evidencing non-Bloch dynamics in temporal topolectrical circuits

One of the core concepts from the non-Hermitian skin effect is the extended complex wavevectors (CW) in the generalized Brillouin zone (GBZ), while the origin of CW remains elusive, and further experimental demonstration of GBZ is still lacking. We show that the bulk states of an open quantum system dynamically governed by the Lindblad master equation exhibit non-Bloch evolution which results in CW. Experimentally, we present temporal topolectrical circuits to serve as simulators for the dynamics of an open system. By reconstructing the correspondence between the bulk states of an open system and circuit voltage modes through gauge scale potentials in the circuit, the non-Bloch evolution is demonstrated. Facilitated by the simulators and proper approach to characterize the non-Bloch band proposed here, the GBZ is confirmed. Our work may advance the investigation of the dissipative topological modes and provide a versatile platform for exploring the unique evolution and topology for both closed and open systems.

Band structures and skin effects of coupled nonreciprocal Su-Schrieffer-Heeger lattices

We pay attention to the influences of the nonreciprocal coupling on the band structures and skin effects in the coupled Su-Schrieffer-Heeger (SSH) lattices. It is shown that the nonreciprocal coupling leads to the non-Hermitian skin effect in a substantial way. Besides, it widens the parameter space of the zero-energy modes in the band gap, and modifies the transition manner from the topologically trivial to topologically nontrivial phase. When the nonreciprocal coupling exceeds its critical value, the zero-energy modes will split, giving rise to the appearance of new nonzero- or complex-energy modes. What is more, differently from the chain configuration, the nonreciprocal coupling makes purely imaginary energy modes emerge in the band gap of the SSH-ring configuration. Next in the presence of hopping disorder, we observe that the zero-energy modes are relatively robust, whereas the imaginary part of energies displays the nonmonotonic changes. It can be thus believed that all these findings promote understanding the influences of nonreciprocal couplings on the types and properties of isolated modes in the SSH lattices.

Tunable non‐Hermitian skin effects in Su‐Schrieffer‐Heeger‐like models

The flourishment of non-Hermitian topology has promoted the development of skin effect, a well-known feature of the non-Hermitian systems, by which the bulk states evolve from extended to localized toward boundaries. However, in previous works, the scenarios are usually delicately designed with intricate parameters to explore the skin effects. In this work, we propose a simple paradigm to implement tunable non-Hermitian skin effects in one and two-dimensional Su-Schrieffer-Heeger (SSH)-like tight-binding models. Skin modes with distinct dimensions can be predicted irrespective of the non-Hermitian systems are topological or not. They also have no relations with the coupling values, but only are dependent on the scaling factors of non-reciprocal hopping terms. Furthermore, by engineering the hopping configurations, the skin modes could be predicted at expected edges or corners, featuring skin effects hierarchical. These tunable non-Hermitian skin effects and higher-dimensional non-Hermitian skin effects can be exploited to guide waves into targeted regions and may have useful applications when realized in metamaterials.

Higher rank chirality and non-Hermitian skin effect in a topolectrical circuit

While chirality imbalances are forbidden in conventional lattice systems, non-Hermiticity can effectively avoid the chiral-doubling theorem to facilitate 1D chiral dynamics. Indeed, such systems support unbalanced unidirectional flows that can lead to the localization of an extensive number of states at the boundary, known as the non-Hermitian skin effect (NHSE). Recently, a generalized (rank-2) chirality describing a 2D robust gapless mode with dispersion ω = kxky has been introduced in crystalline systems. Here we demonstrate that rank-2 chirality imbalances can be established in a non-Hermitian (NH) lattice system leading to momentum-resolved chiral dynamics, and a rank-2 NHSE where there are both edge- and corner-localized skin modes. We then experimentally test this phenomenology in a 2-dimensional topolectric circuit that implements a NH Hamiltonian with a long-lived rank-2 chiral mode. Using impedance measurements, we confirm the rank-2 NHSE in this system, and its manifestation in the predicted skin modes and a highly unusual momentum-position locking response. Our investigation demonstrates a circuit-based path to exploring higher-rank chiral physics, with potential applications in systems where momentum resolution is necessary, e.g., in beamformers and non-reciprocal devices.

Interaction-induced analog of a non-Hermitian skin effect in a lattice two-body problem

We present a theoretical study of the quantum states of two repelling spinless particles in a one-dimensional tight-binding model with a simple periodic lattice and open boundary conditions. We demonstrate that, when the particles are not identical, their interaction drives nontrivial correlated two-particle states, such as bound states and edge states, and induces interaction-induced flat bands. We show that the localization of the center of mass of the two particles enforces the localization of their relative motion, which means formation of the bound states. While the considered system is Hermitian, an insight into the bound states is provided by an approximate effective non-Hermitian model for the relative motion that features the non-Hermitian skin effect.

Nonreciprocal charge and spin transport induced by non-Hermitian skin effect in mesoscopic heterojunctions

The pursuit of the non-Hermitian skin effect (NHSE) in various physical systems is of great research interest. Compared with recent progress in nonelectronic systems, the implementation of the NHSE in condensed matter physics remains elusive. Here, we show that the NHSE can be engineered in the mesoscopic heterojunctions (system plus reservoir) in which electrons in two channels of the system moving towards each other have asymmetric coupling to those of the reservoir. This makes electrons in the system move forward and in the opposite direction have unequal lifetimes, and so gives rise to a point-gap spectral topology. Accordingly, the electron eigenstates exhibit NHSE under the open boundary condition, consistent with the description of the generalized Brillouin zone. Such a reservoir-engineered NHSE visibly manifests itself as the nonreciprocal charge current that can be probed by the standard transport measurements. Further, we generalize the scenario to the spin-resolved NHSE, which can be probed by the nonreciprocal spin transport. Our work opens a research avenue for implementing and detecting the NHSE in electronic mesoscopic systems, which will lead to interesting device applications.