arXiv subjects

Rong Lü

Publications and source records attributed to Rong Lü.

At least 19 recordsLinked to original sources

arXiv2026

Coexistence of topological Anderson insulator and multifractal critical phase in a non-Hermitian quasicrystal

The interplay of topology, disorder, and non-Hermiticity gives rise to phenomena beyond the conventional classification of quantum phases. We propose a one-dimensional non-Hermitian Su-Schrieffer-Heeger model with quasiperiodically modulated nonreciprocal intracell hopping. We show that quasiperiodic modulation can substantially enhance the topological regime and, remarkably, induce a non-Hermitian topological Anderson insulator (TAI) phase. Beyond the topological transition, increasing nonreciprocity drives a cascade of localization transitions in which all bulk eigenstates evolve from extended to multifractal critical and ultimately to localized states. Strikingly, the extended-to-critical transition coincides exactly with a real-complex spectral transition. We establish complete phase diagrams and derive exact analytical boundaries for both topological and localization transitions, uncovering an unanticipated coexistence of TAI and multifractal critical phases. Finally, we propose a feasible implementation in topolectrical circuits. Our results reveal a new paradigm for studying the cooperative effects of topology, quasiperiodicity, and non-Hermiticity.

cond-mat.dis-nn↗

arXiv2026

Topological superconducting phase in a non-Hermitian Kitaev chain with staggered pairing imbalance

We introduce a one-dimensional non-Hermitian Kitaev chain with staggered imbalance in the $p$-wave superconducting pairing. By tuning the chemical potential and the pairing imbalance, we find that the eigenenergy spectrum undergoes real-to-complex transitions, and the spectral gap can change from a real to an imaginary one. The pairing imbalance significantly enlarges the parameter region supporting a topological superconducting phase. Remarkably, we show that a topologically nontrivial phase hosting Majorana zero modes can be induced by varying the pairing imbalance, even in the regime of strong chemical potential. The gap-closing points and phase boundaries are determined analytically, and the resulting phase diagrams are presented with the nontrivial phase characterized by a nonzero topological invariant. Furthermore, we identify the coexistence of Majorana zero modes and finite-energy Majorana edge modes in this system. Our results reveal exotic phenomena arising from imbalanced pairing and establish a platform for exploring topological superconductivity in non-Hermitian systems.

cond-mat.mes-hall↗

arXiv2025

Majorana edge modes in one-dimensional Kitaev chain with staggered $p$-wave superconducting pairing

We introduce a new type of one-dimensional Kitaev chain with staggered $p$-wave superconducting pairing. We find three physical regimes in this model by tuning the $p$-wave pairing and the chemical potential of the system. In the topologically nontrivial phase, there are two Majorana zero modes localized at the opposite ends of the lattice, which are characterized and protected by nonzero topological invariants. More interestingly, we also find a regime where the system can hold four unprotected nonzero-energy edge modes in the trivial phase, which is analogous to a weak topological phase. The third regime is also trivial but holds no edge modes. The emergence of zero- and nonzero-energy edge modes in the system are analyzed by transforming the lattice model into a ladder consisting of Majorana fermions, where the competition between the intra- and inter-leg couplings leads to different phases. We further investigate the properties of edge modes under the influences of dissipation, which is represented by introducing a imaginary part in the chemical potential. Our work unveils the exotic properties induced by the staggered $p$-wave pairing and provides a new platform for further exploration of Majorana edge modes.

cond-mat.mes-hall↗

arXiv2024

Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping

We study the one-dimensional non-Hermitian lattices with linearly varying nonreciprocal hopping, where the non-Hermitian skin effect (NHSE) is found to be dissolved gradually as the strength of nonreciprocity increases. The energy spectrum under the open boundary condition is composed of real and imaginary eigenenergies when the nonreciprocal hopping is weak. Interestingly, the real eigenenergies form an equally spaced ladder, and the corresponding eigenstates are localized at the boundary with a Gaussian distribution due to NHSE. By increasing the nonreciprocity, the number of real eigenenergies will decrease while more and more eigenenergies become imaginary. Accompanied by the real-imaginary transition in the spectrum, the eigenstates are shifted from the boundary into the bulk of the lattice. When the nonreciprocity gets strong enough, the whole spectrum will be imaginary and the NHSE disappears completely in the system; i.e., all the eigenstates become Gaussian bound states localized inside the bulk. Our work unveils the exotic properties of non-Hermitian systems with spatially varying nonreciprocal hopping.

quant-ph↗

arXiv2023

Gaussian eigenstate pinning in non-Hermitian quantum mechanics

We study a one-dimensional system subjected to a linearly varying imaginary vector potential, which is described by the single-particle continuous Schrödinger equation and is analytically solved. The eigenenergy spectrum is found to be real under open boundary condition (OBC) but forms a parabola in the complex energy plane under periodic boundary condition (PBC). The eigenstates always exhibit a modulated Gaussian distribution and are all pinned on the same position, which is determined by the imaginary vector potential and boundary conditions. These behaviors are in sharp contrast to the non-Hermitian skin effect (NHSE) in systems with constant imaginary vector potential, where the eigenstates are exponentially distributed under OBC but become extended under PBC. We further demonstrate that even though the spectrum under PBC is an open curve, the Gaussian type of NHSE still has a topological origin and is characterized by a nonvanishing winding number in the PBC spectrum. The energies interior to the parabola can support localized edge states under semi-infinite boundary condition. The corresponding tight-binding lattice models also show similar properties, except that the PBC spectrum forms closed loops. Our work opens a door for the study of quantum systems with spatially varying imaginary vector potentials.

quant-ph↗

arXiv2022

Real spectra and phase transition of skin effect in nonreciprocal systems

We study the one-dimensional nonreciprocal lattices with real nearest neighboring hopping and find that the energy spectra under open boundary conditions can be entirely real or imaginary. We further investigate the spectral properties and the non-Hermitian skin effect in the one-dimensional mosaic lattices with real nonreciprocal hopping introduced at equally spaced sites. The eigenenergies of such lattices undergo a real-complex-imaginary or real-complex transition as the nonreciprocity varies. Moreover, the skin effect exhibits phase transitions depending on the period of the mosaic nonreciprocity. The bulk states are abruptly shifted from one end of the lattice to the opposite one by crossing the critical points, accompanied by the closing and reopening of point gaps in the spectra under periodic boundary conditions. The phase diagrams of the transition are presented and the critical boundaries are analytically determined. Our work unveils the intriguing properties of the energy spectrum and skin effect in non-Hermitian systems.

quant-ph↗

arXiv2022

Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices

We investigate the spectral topology of one-dimensional lattices where the nonreciprocal hoppings within the nearest $r_d$ neighboring sites are the same. For the purely off-diagonal model without onsite potentials, the energy spectrum of the lattice under periodic boundary conditions (PBCs) forms an inseparable loop that intertwines with itself in the complex energy plane and is characterized by winding numbers ranging from 1 up to $r_d$. The corresponding spectrum under open boundary conditions (OBCs), which is real in the nearest neighboring model, will ramify and take the shape of an $(r_d+1)$-pointed star with all the branches connected at zero energy. If we further introduce periodic onsite modulations, the spectrum will gradually divide into multiple separable bands as we vary the parameters. Most importantly, we find that a different kind of band gap called loop gap can exist in the PBC spectrum, separating an inner loop from an outer one with each composed by part of the spectrum. In addition, loop structures also exist in the OBC spectra of systems with onsite potentials. We further study the lattices with power-law decaying long-range nonreciprocal hopping and found that the intertwined loops in the PBC spectrum will be untangled. Finally, we propose an experimental scheme to realize the long-range nonreciprocal models by exploiting electrical circuits. Our work unveils the exotic spectral topology in the long-range nonreciprocal lattices.

cond-mat.dis-nn↗

arXiv2022

Real spectra, Anderson localization, and topological phases in one-dimensional quasireciprocal systems

We introduce the one-dimensional quasireciprocal lattices where the forward hopping amplitudes between nearest neighboring sites $\{ t+t_{jR} \}$ are chosen to be a random permutation of the backward hopping $\{ t+t_{jL} \}$ or vice versa. The values of $\{ t_{jL} \}$ (or $\{t_{jR} \}$) can be periodic, quasiperiodic, or randomly distributed. We show that the Hamiltonian matrices are pseudo-Hermitian and the energy spectra are real as long as $\{ t_{jL} \}$ (or $\{t_{jR} \}$) are smaller than the threshold value. While the non-Hermitian skin effect is always absent in the eigenstates due to the global cancellation of local nonreciprocity, the competition between the nonreciprocity and the accompanying disorders in hopping amplitudes gives rise to energy-dependent localization transitions. Moreover, in the quasireciprocal Su-Schrieffer-Heeger models with staggered hopping $t_{jL}$ (or $t_{jR}$), topologically nontrivial phases are found in the real-spectra regimes characterized by nonzero winding numbers. Finally, we propose an experimental scheme to realize the quasireciprocal models in electrical circuits. Our findings shed new light on the subtle interplay among nonreciprocity, disorder, and topology.

cond-mat.dis-nn↗

arXiv2021

Topological phases and Anderson localization in off-diagonal mosaic lattices

We introduce a one-dimensional lattice model whose hopping amplitudes are modulated for equally spaced sites. Such mosaic lattice exhibits many interesting topological and localization phenomena that do not exist in the regular off-diagonal lattices. When the mosaic modulation is commensurate with the underlying lattice, topologically nontrivial phases with zero- and nonzero-energy edge modes are observed as we tune the modulation, where the nontrivial regimes are characterized by quantized Berry phases. If the mosaic lattice becomes incommensurate, Anderson localization will be induced purely by the quasiperiodic off-diagonal modulations. The localized eigenstate is found to be centered on two neighboring sites connected by the quasiperiodic hopping terms. Furthermore, both the commensurate and incommensurate off-diagonal mosaic lattices can host Chern insulators in their two-dimensional generalizations. Our work provides a platform for exploring topological phases and Anderson localization in low-dimensional systems.

cond-mat.dis-nn↗

arXiv2020

Topological Superconductors in One-Dimensional Mosaic Lattices

We study topological superconductor in one-dimensional (1D) mosaic lattice whose on-site potentials are modulated for equally spaced sites. When the system is topologically nontrivial, Majorana zero modes appear at the two ends of the 1D lattice. By calculating energy spectra and topological invariant of the system, we find the interval of the mosaic modulation of the on-site potential, whether it is periodic, quasiperiodic, or randomly distributed, can influence the topological properties significantly. For even interval of the mosaic potential, the system will always exist in the topological superconducting phase for any finite on-site potentials. When the interval is odd, the system undergoes a topological phase transition and enters into the trivial phase as the on-site potentials become stronger than a critical value, except for some special cases in the commensurate lattices. These conclusions are proven and the phase boundaries determined analytically by exploiting the method of transfer matrix. They reveal that robust Majorana zero modes can arise in 1D mosaic lattice independent of the strength of the spatially modulated potentials.

cond-mat.dis-nn↗

arXiv2020

Topological invariants, zero mode edge states and finite size effect for a generalized non-reciprocal Su-Schrieffer-Heeger model

Intriguing issues in one-dimensional non-reciprocal topological systems include the breakdown of usual bulk-edge correspondence and the occurrence of half-integer topological invariants. In order to understand these unusual topological properties, we investigate the topological phase diagrams and the zero-mode edge states of a generalized non-reciprocal Su-Schrieffer-Heeger model, based on some analytical results. Meanwhile, we provide a concise geometrical interpretation of the bulk topological invariants in terms of two independent winding numbers and also give an alternative interpretation related to the linking properties of curves in three-dimensional space. For the system under the open boundary condition, we construct analytically the wavefunctions of zero-mode edge states by properly considering a hidden symmetry of the system and the normalization condition with the use of biorthogonal eigenvectors. Our analytical results directly give the phase boundary for the existence of zero-mode edge states and unveil clearly the evolution behavior of edge states. In comparison with results via exact diagonalization of finite-size systems, we find our analytical results agree with the numerical results very well.

cond-mat.mes-hall↗

arXiv2020

The $D\to ρ$ semileptonic and radiative decays within the light-cone sum rules

The measured branching ratio of the $D$ meson semileptonic decay $D \to ρe^+ ν_e$, which is based on the $0.82~{\rm fb^{-1}}$ CLEO data taken at the peak of $ψ(3770)$ resonance, disagrees with the traditional SVZ sum rules analysis by about three times. In the paper, we show that this discrepancy can be eliminated by applying the QCD light-cone sum rules (LCSR) approach to calculate the $D\to ρ$ transition form factors $A_{1,2}(q^2)$ and $V(q^2)$. After extrapolating the LCSR predictions of these TFFs to whole $q^2$-region, we obtain $1/|V_{\rm cd}|^2 \times Γ(D \to ρe ν_e) =(55.45^{+13.34}_{-9.41})\times 10^{-15}~{\rm GeV}$. Using the CKM matrix element and the $D^0(D^+)$ lifetime from the Particle Data Group, we obtain ${\cal B} (D^0\to ρ^- e^+ ν_e) = (1.749^{+0.421}_{-0.297}\pm 0.006)\times 10^{-3}$ and ${\cal B} (D^+ \to ρ^0 e^+ ν_e) = (2.217^{+0.534}_{-0.376}\pm 0.015)\times 10^{-3}$, which agree with the CLEO measurements within errors. We also calculate the branching ratios of the two $D$ meson radiative processes and obtain ${\cal B}(D^0\to ρ^0 γ)= (1.744^{+0.598}_{-0.704})\times 10^{-5}$ and ${\cal B}(D^+ \to ρ^+ γ) = (5.034^{+0.939}_{-0.958})\times 10^{-5}$, which also agree with the Belle measurements within errors. Thus we think the LCSR approach is applicable for dealing with the $D$ meson decays.

hep-ph↗

arXiv2018

Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems

We unveil the geometrical meaning of winding number and utilize it to characterize the topological phases in one-dimensional chiral non-Hermitian systems. While chiral symmetry ensures the winding number of Hermitian systems being integers, it can take half integers for non-Hermitian systems. We give a geometrical interpretation of the half integers by demonstrating that the winding number $ν$ of a non-Hermitian system is equal to half of the summation of two winding numbers $ν_1$ and $ν_2$ associated with two exceptional points respectively. The winding numbers $ν_1$ and $ν_2$ represent the times of real part of the Hamiltonian in momentum space encircling the exceptional points and can only take integers. We further find that the difference of $ν_1$ and $ν_2$ is related to the second winding number or energy vorticity. By applying our scheme to a non-Hermitian Su-Schrieffer-Heeger model and an extended version of it, we show that the topologically different phases can be well characterized by winding numbers. Furthermore, we demonstrate that the existence of left and right zero-mode edge states is closely related to the winding number $ν_1$ and $ν_2$.

cond-mat.mes-hall↗

arXiv2017

Quench dynamics in the Aubry-André-Harper model with \textit{p}-wave superconductivity

The Anderson localization phase transition in the Aubry-André-Harper (AAH) model with \textit{p}-wave superconducting (SC) pairing is numerically investigated by suddenly changing the on-site potential from zero to various finite values which fall into the extended, critical and localized phase regimes shown in this model. The time evolutions of entanglement entropy (EE), mean width of wave packets and Loschmidt echo of the system exhibit distinct but consistent dynamical signatures in those three phases. Specifically, the EE grows as a power function of time with the exponent of which varies in the extended phase but keeps almost unchanged in the critical phase for different quench parameters. However, if the system is in the localized phase after a quench, the EE grows much slower and will soon get saturated. The time-dependent width of wave packets in the system shows similar behaviors as the EE. In addition, from the perspective of dynamical phase transition, we find that the Loschmidt echo oscillates and always keeps finite when the system is quenched in the extended phase. In contrast, in the critical or localized phase, the echo will reach to zero at some time intervals or will decay almost to zero after a long-time evolution. The universal features of these quantities in the critical phase of the system with various SC pairing amplitudes are also observed.

cond-mat.dis-nn↗

arXiv2017

Observation of "broad" d-wave Feshbach resonances with a triplet structure

High partial-wave ($l\ge2$) Feshbach resonance (FR) in an ultracold mixture of $^{85}$Rb-$^{87}$Rb atoms is investigated experimentally aided by a partial-wave insensitive analytic multichannel quantum-defect theory (MQDT). Two "broad" resonances from coupling between d-waves in both the open and closed channels are observed and characterized. One of them shows a fully resolved triplet structure with splitting ratio well explained by the perturbation to the closed channel due to interatomic spin-spin interaction. These tunable "broad" d-wave resonances, especially the one in the lowest-energy open channel, could find important applications in simulating d-wave coupling dominated many-body systems. In addition, we find that there is generally a time and temperature requirement, associated with tunneling through the angular momentum barrier, to establish and observe resonant coupling in nonzero partial waves.

cond-mat.quant-gas↗

arXiv2017

Anderson localization in the Non-Hermitian Aubry-André-Harper model with physical gain and loss

We investigate the Anderson localization in non-Hermitian Aubry-André-Harper (AAH) models with imaginary potentials added to lattice sites to represent the physical gain and loss during the interacting processes between the system and environment. By checking the mean inverse participation ratio (MIPR) of the system, we find that different configurations of physical gain and loss have very different impacts on the localization phase transition in the system. In the case with balanced physical gain and loss added in an alternate way to the lattice sites, the critical region (in the case with p-wave superconducting pairing) and the critical value (both in the situations with and without p-wave pairing) for the Anderson localization phase transition will be significantly reduced, which implies an enhancement of the localization process. However, if the system is divided into two parts with one of them coupled to physical gain and the other coupled to the corresponding physical loss, the transition process will be impacted only in a very mild way. Besides, we also discuss the situations with imbalanced physical gain and loss and find that the existence of random imaginary potentials in the system will also affect the localization process while constant imaginary potentials will not.

cond-mat.dis-nn↗

arXiv2017

Transport through a non-Hermitian Aharonov-Bohm ring with physical gain and loss

We investigate a non-Hermitian Aharonov-Bohm (AB) ring system with a quantum dot (QD) embedded in each of its two arms. The energy levels of the QDs are complex in order to take into account the physical gain or loss of the ring system during its interacting processes with the environment. When there is magnetic flux threading through the ring, by allocating the flux phase factor into the tunneling amplitudes between the QDs and the leads in different ways, the Hamiltonian of the system can be written into different formalisms. We calculate the transmission through the ring by using these different non-Hermitian Hamiltonians and prove that it is not dependent on the way we treat the phase factor, as in the Hermitian case. In addition, with appropriate parameters, the asymmetric Fano profile will show up in the conductance spectrum just by tuning the physical gain and loss of the system. The Fano effect originates from the interferences of electrons traversing different channels which are broadened or narrowed down due to the interaction between the QDs and the environment. The proof we provide and the transport properties revealed in this paper demonstrate the influences of the environment on an otherwise isolated system and pave the way for the further studies on non-Hermitian AB ring systems.

quant-ph↗

arXiv2016

Generalized Aubry-André-Harper model with p-wave superconducting pairing

We investigate a generalized Aubry-André-Harper (AAH) model with p-wave superconducting pairing. Both the hopping amplitudes between the nearest neighboring lattice sites and the on-site potentials in this system are modulated by a cosine function with a periodicity of $1/α$. In the incommensurate case [$α=(\sqrt{5}-1)/2$], due to the modulations on the hopping amplitudes, the critical region of this quasiperiodic system is significantly reduced and the system becomes more easily to be turned from extended states to localized states. In the commensurate case ($α= 1/2$), we find that this model shows three different phases when we tune the system parameters: Su-Schrieffer-Heeger (SSH)-like trivial, SSH-like topological, and Kitaev-like topological phases. The phase diagrams and the topological quantum numbers for these phases are presented in this work. This generalized AAH model combined with superconducting pairing provides us with a useful testfield for studying the phase transitions from extended states to Anderson localized states and the transitions between different topological phases.

cond-mat.str-el↗