Spectral Structure and Doublon Dissociation in the Two-Particle Non-Hermitian Hubbard Model

Strongly-correlated systems in non-Hermitian models are an emergent area of research. Herein, a non-Hermitian Hubbard model is considered, where the single-particle hopping amplitudes on the lattice are not reciprocal, and provide exact analytical results of the spectral structure in the two-particle sector of Hilbert space under different boundary conditions. The analysis unveils some interesting spectral and dynamical effects of purely non-Hermitian nature and that deviate from the usual scenario found in the single-particle regime. Specifically, a spectral phase transition of the Mott-Hubbard band on the infinite lattice is predicted as the interaction energy is increased above a critical value, from an open to a closed loop in complex energy plane, and the dynamical dissociation of doublons, i.e., instability of two-particle bound states, in the bulk of the lattice, with a sudden revival of the doublon state when the two particles reach the lattice edge. Particle dissociation observed in the bulk of the lattice is a clear manifestation of non-Hermitian dynamics arising from the different lifetimes of single-particle and two-particle states, whereas the sudden revival of the doublon state at the boundaries is a striking burst edge dynamical effect peculiar to non-Hermitian systems with boundary-dependent energy spectra, here predicted for the first time for correlated particles.     

Topological properties of non-Hermitian Creutz ladders

We study topological properties of the one-dimensional Creutz ladder model with different non-Hermitian asymmetric hoppings and on-site imaginary potentials,and obtain phase diagrams regarding the presence and absence of an energy gap and in-gap edge modes.The non-Hermitian skin effect(NHSE),which is known to break the bulk-boundary correspondence(BBC),emerges in the system only when the non-Hermiticity induces certain unbalanced non-reciprocity along the ladder.The topological properties of the model are found to be more sophisticated than that of its Hermitian counterpart,whether with or without the NHSE.In one scenario without the NHSE,the topological winding is found to exist in a two-dimensional plane embedded in a four-dimensional space of the complex Hamiltonian vector.The NHSE itself also possesses some unusual behaviors in this system,including a high spectral winding without the presence of long-range hoppings,and a competition between two types of the NHSE,with the same and opposite inverse localization lengths for the two bands,respectively.Furthermore,it is found that the NHSE in this model does not always break the conventional BBC,which is also associated with whether the band gap closes at exceptional points under the periodic boundary condition.     

Efficient and stable wireless power transfer based on the non-Hermitian physics

As one of the most attractive non-radiative power transfer mechanisms without cables,efficient magnetic resonance wireless power transfer(WPT)in the near field has been extensively developed in recent years,and promoted a variety of practical applications,such as mobile phones,medical implant devices and electric vehicles.However,the physical mechanism behind some key limitations of the resonance WPT,such as frequency splitting and size-dependent efficiency,is not very clear under the widely used circuit model.Here,we review the recently developed efficient and stable resonance WPT based on non-Hermitian physics,which starts from a completely different avenue(utilizing loss and gain)to introduce novel functionalities to the resonance WPT.From the perspective of non-Hermitian photonics,the coherent and incoherent effects compete and coexist in the WPT system,and the weak stable of energy transfer mainly comes from the broken phase associated with the phase transition of parity-time symmetry.Based on this basic physical framework,some optimization schemes are proposed,including using nonlinear effect,using bound states in the continuum,or resorting to the system with high-order parity-time symmetry.Moreover,the combination of non-Hermitian physics and topological photonics in multi-coil system also provides a versatile platform for long-range robust WPT with topological protection.Therefore,the non-Hermitian physics can not only exactly predict the main results of current WPT systems,but also provide new ways to solve the difficulties of previous designs.     

Edge states enhanced by long-range hopping: An analytical study

We analyze the behavior of edge states in long-range(LR) interacting systems. In terms of lattice model Hamiltonian with the LR coupling, we determine analytically the condition of existence of edge states within the transfer matrix method(TMM). The expressions we obtain are general and hold for any choice of the LR hopping. The reason why edge states can appear is the transfer matrix in the bulk different from that in the boundary layers. Our predictions are in good agreement with numerical results by exact diagonalization. Our result is helpful in solving novel edge states in oneand two-dimensional(2D) superconductors with LR hopping and pairing.     

Investigating the nonequilibrium aspects of long-range Potts model: Refinement of critical temperatures and raw exponents

In this work, we analyze the q-state Potts model with long-range interactions through nonequilibrium scaling relations commonly used when studying short-range systems. We determine the critical temperature via an optimization method for short-time Monte Carlo simulations. The study takes into consideration two different boundary conditions and three different values of range parameters of the couplings. We also present estimates of some critical exponents, named as raw exponents for systems with long-range interactions, which confirm the non-universal character of the model. Finally, we provide some preliminary results addressing the relations between the raw exponents and the exponents obtained for systems with short-range interactions. The results assert that the methods employed in this work are suitable to study the considered model and can easily be adapted to other systems with long-range interactions.     

聚二乙炔电子特性研究

将聚二乙炔主链简化为有限的一维复式碳原子链,利用紧束缚近似,在周期性和非周期性边界条件下,考虑π电子在最近邻的跳跃,计算和分析了不同数目聚二乙炔单体聚合而成的有限一维原子链的能谱和态密度,揭示了聚二乙炔电子结构的基本特点.     

Real non-Hermitian energy spectra without any symmetry

Non-Hermitian models with real eigenenergies are highly desirable for their stability. Yet, most of the currently known ones are constrained by symmetries such as PT-symmetry, which is incompatible with realizing some of the most exotic non-Hermitian phenomena. In this work, we investigate how the non-Hermitian skin effect provides an alternative route towards enforcing real spectra and system stability. We showcase, for different classes of energy dispersions, various ansatz models that possess large parameter space regions with real spectra, despite not having any obvious symmetry. These minimal local models can be quickly implemented in non-reciprocal experimental setups such as electrical circuits with operational amplifiers.     

Nondiffracting wave beams in non-Hermitian Glauber–Fock lattice

We theoretically study non-Hermitian Glauber–Fock lattice with nonuniform hopping. We show how to engineer this lattice to get nondiffracting wave beams and find an exact analytical solution to nondiffracting localized waves. The exceptional points in the energy spectrum are also analyzed.     

Non-Hermitian quasicrystal in dimerized lattices

Non-Hermitian quasicrystals possess PT and metal–insulator transitions induced by gain and loss or nonreciprocal effects. In this work, we uncover the nature of localization transitions in a generalized Aubry–André–Harper model with dimerized hopping amplitudes and complex onsite potential. By investigating the spectrum, adjacent gap ratios and inverse participation ratios, we find an extended phase, a localized phase and a mobility edge phase, which are originated from the interplay between hopping dimerizations and non-Hermitian onsite potential. The lower and upper bounds of the mobility edge are further characterized by a pair of topological winding numbers, which undergo quantized jumps at the boundaries between different phases. Our discoveries thus unveil the richness of topological and transport phenomena in dimerized non-Hermitian quasicrystals.     

具有p波超流的一维非公度晶格中迁移率边研究

研究了具有p波超流的一维非公度晶格中迁移率边的性质. 发现适当的p波超流可以增加体系中的迁移率边的数目, 并且通过多分形分析确定了迁移率边所在的位置.     

Mobility edges and reentrant localization in one-dimensional dimerized non-Hermitian quasiperiodic lattice

The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with nonHermitian either uniform or staggered quasiperiodic potentials.We find that the non-Hermitian uniform quasiperiodic disorder can induce an intermediate phase where the extended states coexist with the localized ones,which implies that the system has mobility edges.The localization transition is accompanied by the PT symmetry breaking transition.While if the non-Hermitian quasiperiodic disorder is staggered,we demonstrate the existence of multiple intermediate phases and multiple reentrant localization transitions based on the finite size scaling analysis.Interestingly,some already localized states will become extended states and can also be localized again for certain non-Hermitian parameters.The reentrant localization transitions are associated with the intermediate phases hosting mobility edges.Besides,we also find that the non-Hermiticity can break the reentrant localization transition where only one intermediate phase survives.More detailed information about the mobility edges and reentrant localization transitions are presented by analyzing the eigenenergy spectrum,inverse participation ratio,and normalized participation ratio.     

Topological quantum phase transition in 5d transition metal oxide Na2IrO3

We predict a quantum phase transition from normal to topological insulators in the 5d transition metal oxide Na2IrO3, where the transition can be driven by the change of the long-range hopping and trigonal crystal field terms. From the first-principles-derived tight-binding Hamiltonian, we determine the phase boundary through the parity analysis. In addition, our first-principles calculations for Na2IrO3 model structures show that the interlayer distance can be an important parameter for the existence of a three-dimensional strong topological insulator phase. Na2IrO3 is suggested to be a candidate material which can have both a nontrivial topology of bands and strong electron correlations.     

Topological Phase Transition with Larger Winding Number in the Non-Hermitian Dimerized Lattice

The topological phase transitions among normal insulator phase, two kinds of topological insulator phases, and topological semimetal phase are shown based on the non-Hermitian dimerized Su–Schrieffer–Heeger (SSH) model with the nonreciprocal intercell and long-range hopping. In contrast to the previous work, it is found that the topological insulator phase in the present SSH model can hold the larger non-Bloch winding number accompanied by exceptional winding of the generalized Brillouin zone around the gap-closing points. Compared with the usual topological insulator phase in non-Hermitian SSH model, the topological insulator with the larger winding number owns two pairs of zero energy modes with a distinct form of edge localization in the gap. The physical mechanism of the distinct edge localization for zero energy modes via a equivalent Hermitian version of the non-Hermitian SSH model is revealed. Additionally, the process of the phase transition is visualized among normal insulator phase, topological insulator phases, and topological semimetal phase in detail via the evolution of the gap-closing points on the plane of generalized Brillouin zone. This work further verifies the non-Bloch theory and enrich the investigation about the topologically nontrivial phase with the larger topological invariant in the non-Hermitian SSH model.     

Nonlinear dispersion of a pollutant ejected into a channel flow

In this paper, we study the nonlinear coupled boundary value problem arising from the nonlinear dispersion of a pollutant ejected by an external source into a channel flow. We obtain exact solutions for the steady flow for some special cases and an implicit exact solution for the unsteady flow. Additionally, we obtain analytical solutions for the transient flow. From the obtained solutions, we are able to deduce the qualitative influence of the model parameters on the solutions. Furthermore, we are able to give both exact and analytical expressions for the skin friction and wall mass transfer rate as functions of the model parameters. The model considered can be useful for understanding the polluting situations of an improper discharge incident and evaluating the effects of decontaminating measures for the water bodies.     

Existence of positive solutions for nonlocal boundary value problem of fractional differential equation

In this paper, we study a type of nonlinear fractional differential equations multi-point boundary value problem with fractional derivative in the boundary conditions. By using the upper and lower solutions method and fixed point theorems, some results for the existence of positive solutions for the boundary value problem are established. Some examples are also given to illustrate our results.     

Helmholtz free energy of a multilayer system of highly charged plates immersed in an electrolyte

The Helmholtz free energy of highly charged plates immersed in an electrolyte solution in a finite container is investigated using mean field theory. Exact solutions of the Poisson-Boltzmann equation under Dirichlet and Neumann boundary conditions lead to analytical expressions for the free energies. Adiabatic potentials of the charged plates, which are derived from the free energy, have long-range weak attractive parts and medium-range strong repulsive parts, irrespective of the type of boundary conditions. The repulsion results mainly from the osmotic pressure of the excess ions trapped between the plates by the large surface charges and the attraction arises essentially from an electric pull from the intermediate cloud of excess counterions shared by the plates.     

Non-Hermitian systems of Euclidean Lie algebraic type with real energy spectra

We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean–Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries exhibiting various types of qualitative behaviour. On the basis of explicitly computed non-perturbative Dyson maps we construct metric operators, isospectral Hermitian counterparts for which we solve the corresponding time-independent Schrödinger equation for specific choices of the coupling constants. In these cases general analytical expressions for the solutions are obtained in the form of Mathieu functions, which we analyze numerically to obtain the corresponding energy spectra. We identify regions in the parameter space for which the corresponding spectra are entirely real and also domains where the PT symmetry is spontaneously broken and sometimes also regained at exceptional points. In some cases it is shown explicitly how the threshold region from real to complex spectra is characterized by the breakdown of the Dyson maps or the metric operator. We establish the explicit relationship to models currently under investigation in the context of beam dynamics in optical lattices.     

Many-electron Coulomb correlations in hopping transport along layers of quantum dots

Experimental data are analyzed on the hopping transport of holes in two-dimensional layers of Ge/Si(001) quantum dots (QDs) under conditions of the long-range Coulomb interaction of charge carriers localized in QDs, when the temperature dependence of the conductivity obeys the Efros-Shklovskii law. It is found that the parameters of hopping conduction significantly deviate from the predictions of the model of one-electron excitations in “Coulomb glasses.” Many-particle Coulomb correlations associated with the motion of holes localized in QDs play a decisive role in the processes of hopping charge transfer between QDs. These correlations lead to a substantial decrease in the Coulomb barriers for the tunneling of charge carriers.     

Topological and dynamical phase transitions in the Su–Schrieffer–Heeger model with quasiperiodic and long-range hoppings

Disorders and long-range hoppings can induce exotic phenomena in condensed matter and artificial systems. We study the topological and dynamical properties of the quasiperiodic Su–Schrier–Heeger model with long-range hoppings. It is found that the interplay of quasiperiodic disorder and long-range hopping can induce topological Anderson insulator phases with non-zero winding numbers $\omega =1,2,$ and the phase boundaries can be consistently revealed by the divergence of zero-energy mode localization length. We also investigate the nonequilibrium dynamics by ramping the long-range hopping along two different paths. The critical exponents extracted from the dynamical behavior agree with the Kibble–Zurek mechanic prediction for the path with $W=0.90.$ In particular, the dynamical exponent of the path crossing the multicritical point is numerical obtained as $1/6{\rm{\sim }}0.167,$ which agrees with the unconventional finding in the previously studied XY spin model. Besides, we discuss the anomalous and non-universal scaling of the defect density dynamics of topological edge states in this disordered system under open boundary condictions.     

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.