Complex energy plane and topological invariant in non-Hermitian systems

Non-Hermitian systems as theoretical models of open or dissipative systems exhibit rich novel physical properties and fundamental issues in condensed matter physics. We propose a generalized local–global correspondence between the pseudo-boundary states in the complex energy plane and topological invariants of quantum states. We find that the patterns of the pseudo-boundary states in the complex energy plane mapped to the Brillouin zone are topological invariants against the parameter deformation. We demonstrate this approach by the non-Hermitian Chern insulator model. We give the consistent topological phases obtained from the Chern number and vorticity. We also find some novel topological invariants embedded in the topological phases of the Chern insulator model, which enrich the phase diagram of the non-Hermitian Chern insulators model beyond that predicted by the Chern number and vorticity. We also propose a generalized vorticity and its flipping index to understand physics behind this novel local–global correspondence and discuss the relationships between the local–global correspondence and the Chern number as well as the transformation between the Brillouin zone and the complex energy plane. These novel approaches provide insights to how topological invariants may be obtained from local information as well as the global property of quantum states, which is expected to be applicable in more generic non-Hermitian systems.     

A new way to construct topological invariants of non-Hermitian systems with the non-Hermitian skin effect

The non-Hermitian skin effect breaks the conventional bulk–boundary correspondence and leads to non-Bloch topological invariants. Inspired by the fact that the topological protected zero modes are immune to perturbations, we construct a partner of a non-Hermitian system by getting rid of the non-Hermitian skin effect. Through adjusting the imbalance hopping, we find that the existence of zero-energy boundary states still dictate the bulk topological invariants based on the band-theory framework. Two non-Hermitian Su–Schrieffer–Heeger(SSH) models are used to illuminate the ideas. Specially, we obtain the winding numbers in analytical form without the introduction of the generalized Brillouin zone. The work gives an alternative method to calculate the topological invariants of non-Hermitian systems.     

Observation of an acoustic non-Hermitian topological Anderson insulator

The interaction of band topology and disorder can give rise to intriguing phenomena. One paradigmatic example is the topological Anderson insulator, whose nontrivial topology is induced in a trivial system by disorders. In this study, we investigate the efect of purely non-Hermitian disorders on topological systems using a one-dimensional acoustic lattice with coupled resonators. Specifically, we construct a theoretical framework to describe the non-Hermitian topological Anderson insulator phase...     

Exact mobility edges and topological phase transition in two-dimensional non-Hermitian quasicrystals

The emergence of the mobility edge(ME)has been recognized as an important characteristic of Anderson localization.The difficulty in understanding the physics of the MEs in three-dimensional(3 D)systems from a microscopic image encourages the development of models in lower-dimensional systems that have exact MEs.While most of the previous studies are concerned with one-dimensional(1 D)quasiperiodic systems,the analytic results that allow for an accurate understanding of two-dimensional(2 D)cases are rare.In this work,we disclose an exactly solvable 2 D quasicrystal model with parity-time(PT)symmetry displaying exact MEs.In the thermodynamic limit,we unveil that the extended-localized transition point,observed at the PT symmetry breaking point,is topologically characterized by a hidden winding number defined in the dual space.The coupling waveguide platform can be used to realize the 2 D non-Hermitian quasicrystal model,and the excitation dynamics can be used to detect the localization features.     

Biorthogonal quantum criticality in non-Hermitian many-body systems

We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of the ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a second-order phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.     

Topological Anderson insulator in two-dimensional non-Hermitian systems

We study the disorder-induced phase transition in two-dimensional non-Hermitian systems. First, the applicability of the noncommutative geometric method(NGM) in non-Hermitian systems is examined. By calculating the Chern number of two different systems(a square sample and a cylindrical one), the numerical results calculated by NGM are compared with the analytical one, and the phase boundary obtained by NGM is found to be in good agreement with the theoretical prediction. Then, we use NGM to investigate the evolution of the Chern number in non-Hermitian samples with the disorder effect. For the square sample, the stability of the non-Hermitian Chern insulator under disorder is confirmed. Significantly,we obtain a nontrivial topological phase induced by disorder. This phase is understood as the topological Anderson insulator in non-Hermitian systems. Finally, the disordered phase transition in the cylindrical sample is also investigated. The clean non-Hermitian cylindrical sample has three phases, and such samples show more phase transitions by varying the disorder strength:(1) the normal insulator phase to the gapless phase,(2) the normal insulator phase to the topological Anderson insulator phase, and(3) the gapless phase to the topological Anderson insulator phase.     

Minimal length in quantum mechanics and non-Hermitian Hamiltonian systems

Deformations of the canonical commutation relations lead to non-Hermitian momentum and position operators and therefore almost inevitably to non-Hermitian Hamiltonians. We demonstrate that such type of deformed quantum mechanical systems may be treated in a similar framework as quasi/pseudo and/or -symmetric systems, which have recently attracted much attention. For a newly proposed deformation of exponential type we compute the minimal uncertainty and minimal length, which are essential in almost all approaches to quantum gravity.     

Application of non-Hermitian Hamiltonian model in open quantum optical systems

Non-Hermitian systems have observed numerous novel phenomena and might lead to various applications. Unlike standard quantum physics, the conservation of energy guaranteed by the closed system is broken in the non-Hermitian system, and the energy can be exchanged between the system and the environment. Here we present a scheme for simulating the dissipative phase transition with an open quantum optical system. The competition between the coherent interaction and dissipation leads to the second-order phase transition. Furthermore, the quantum correlation in terms of squeezing is studied around the critical point. Our work may provide a new route to explore the non-Hermitian quantum physics with feasible techniques in experiments.     

Controlling decoherence via PT-symmetric non-Hermitian open quantum systems

We have studied the effect of a non-Hermitian Bosonic bath on the dynamics of a two-level spin system. The non-Hermitian Hamiltonian of the bath is chosen such that it converges to the harmonic oscillator Hamiltonian when the non-Hermiticity is switched off. We calculate the dynamics of the spin system and found that the non-Hermiticity can have positive as well as negative effects on the coherence of the system. However, the decoherence can be completely eliminated by choosing the non-Hermiticity parameter and the phase of the system bath interaction appropriately. We have also studied the effect of this bath on the entanglement of a two-spin system when the bath is acting only on one spin.     

Characterizing entanglement in non-Hermitian chaotic systems via out-of-time ordered correlators

We investigate the quantum entanglement in a non-Hermitian kicking system. In the Hermitian case, the out-of-time ordered correlators (OTOCs) exhibit the unbounded power-law increase with time. Correspondingly, the linear entropy, which is a common measurement of entanglement, rapidly increases from zero to almost unity, indicating the formation of quantum entanglement. For strong enough non-Hermitian driving, both the OTOCs and linear entropy rapidly saturate as time evolves. Interestingly, with the increase of non-Hermitian kicking strength, the long-time averaged value of both OTOCs and linear entropy has the same transition point where they exhibit the sharp decrease from a plateau, demonstrating the disentanglment. We reveal the mechanism of disentanglement with the extension of Floquet theory to non-Hermitian systems.     

Application of Lie transform perturbation method for multidimensional non-Hermitian systems

Three-dimensional non-Hermitian systems are investigated using classical perturbation theory based on Lie transformations. Analytic expressions for total energy in terms of action variables are derived. Both real and complex semiclassical eigenvalues are obtained by quantizing the action variables. It was found that semiclassical energy eigenvalues calculated with the classical perturbation theory are in very good agreement with exact energies and for certain non-Hermitian systems second-order classical perturbation theory performed better than the second-order Rayleigh–Schroedinger perturbation theory.     

Time evolution of non-Hermitian quantum systems and generalized master equations

We inquire into the time evolution of quantum systems associated with pseudo-or quasi-Hermitian Hamiltonians. We obtain, in the pseudo-Hermitian case, a generalized Liouville-von Neumann equation for closed systems. We show that quantum systems with quasi-Hermitian Hamiltonians admit the proper interpretation in terms of open quantum system and derive a generalized Lindblad-Kossakowski equation. Finally, we extend such formalism to the study of decaying systems. Partially supported by PRIN “Sintesi”.     

Eigenvalue crossings in Floquet topological systems

Letters in Mathematical Physics - The topology of electrons on a lattice subject to a periodic driving is captured by the three-dimensional winding number of the propagator that describes time...     

Observation of a topological relaxation mode in microemulsions

We report the observation of two diffusive relaxation modes in a very swollen microemulsion, measured by quasielastic light scattering experiments. In addition to a short-time diffusion process, we observe a long-time diffusive relaxation mode with unusual scaling behavior: the diffusion constant D is an exponential function of the characteristic length scale xi, D~exp(-xi). This observation provides experimental evidence for thermally activated topological relaxation of random fluid phases, as predicted by Milner et al. [J. Phys. (Paris) 51, 2629 (1990)]. We describe the activation energy of such a process by some simple microscopic model for the surfactant layer and give an estimation of the membrane elastic and Gaussian moduli kappa and kappa;, and its spontaneous curvature.     

Entanglement in non-Hermitian quantum theory

Entanglement is one of the key features of quantum world that has no classical counterpart. This arises due to the linear superposition principle and the tensor product structure of the Hilbert space when we deal with multiparticle systems. In this paper, we will introduce the notion of entanglement for quantum systems that are governed by non-Hermitian yet PT-symmetric Hamiltonians. We will show that maximally entangled states in usual quantum theory behave like non-maximally entangled states in PT-symmetric quantum theory. Furthermore, we will show how to create entanglement between two PT qubits using non-Hermitian Hamiltonians and discuss the entangling capability of such interaction Hamiltonians that are non-Hermitian in nature.     

Some topological states in one-dimensional cold atomic systems

Ultracold atoms trapped in optical lattices nowadays have been widely used to mimic various models from condensed-matter physics. Recently, many great experimental progresses have been achieved for producing artificial magnetic field and spin–orbit coupling in cold atomic systems, which turn these systems into a new platform for simulating topological states. In this paper, we give a review focusing on quantum simulation of topologically protected soliton modes and topological insulators in one-dimensional cold atomic system. Firstly, the recent achievements towards quantum simulation of one-dimensional models with topological non-trivial states are reviewed, including the celebrated Jackiw–Rebbi model and Su–Schrieffer–Heeger model. Then, we will introduce a dimensional reduction method for systematically constructing high dimensional topological states in lower dimensional models and review its applications on simulating two-dimensional topological insulators in one-dimensional optical superlattices.     

Observation of dirac holes and electrons in a topological insulator

We show that in the new topological-insulator compound Bi(1.5)Sb(0.5)Te(1.7)Se(1.3) one can achieve a surfaced-dominated transport where the surface channel contributes up to 70% of the total conductance. Furthermore, it was found that in this material the transport properties sharply reflect the time dependence of the surface chemical potential, presenting a sign change in the Hall coefficient with time. We demonstrate that such an evolution makes us observe both Dirac holes and electrons on the surface, which allows us to reconstruct the surface band dispersion across the Dirac point.     

Stress induced topological fluctuations in confined lamellar systems

We investigate the role of defects in a model order-disorder transition, the lamellar-microemulsion transition. We focus on the effect of an applied external stress on the transition mechanism. We first analyse the thermodynamical consistency of the usual Landau-Ginzburg modelling of these systems, and show that thermodynamical, mechanical and structural quantities can all be probed at the same time, which allows for a deeper understanding of the transition mechanisms. We apply this formalism to the case of a lamellar system confined between two plates, the model geometry for a surface force apparatus.