arXiv subjects

Linhu Li

Publications and source records attributed to Linhu Li.

At least 37 records · Page 2Linked to original sources

arXiv2024

Non-Hermitian skin effect in fragmented Hilbert spaces of one-dimensional fermionic lattices

We discover that the interplay between Hilbert space fragmentation and multiple non-Hermitian pumping channels leads to distinct non-Hermitian skin effect (NHSE) in real and Fock spaces. Using an extended Hatano-Nelson model with next-nearest neighbor hopping and a strong interaction as an example, we find that two fermions loaded in the lattice exhibit different real-space NHSE depending on the Hilbert space fragments they belong to. Moreover, in the high-energy sector resulting from the fragmentation, the two-particle bound states form a one-dimensional lattice in Fock space, resulting in the Fock-space NHSE. At half-filling, while real-space NHSE is suppressed by many-body effects, richer patterns of Fock-space skin-like localization are found to emerge for different fragmented energy sectors and subsectors. This work extends our understanding of the interplay between NHSE and Hilbert space fragmentation and provides detailed insights into their manifestation in interacting non-Hermitian systems.

cond-mat.quant-gas↗

arXiv2024

Multiple topological transitions and spectral singularities in non-Hermitian Floquet systems

The interplay between Floquet driving and non-Hermitian gain/loss could give rise to intriguing phenomena including topological funneling of light, edge-state delocalization, anomalous topological transitions and Floquet non-Hermitian skin effects. In this work, we uncover two unique phenomena in Floquet systems caused by gain and loss. First, multiple topological transitions from anomalous Floquet second-order topological insulators to anomalous Floquet first-order topological insulators and then to normal insulators can be induced by gain and loss. Interestingly, the resulting anomalous Floquet insulators further carry hybrid skin-topological boundary modes, which could either be fully localized or localized to different edges at different time slices and traversing along all edges in a single driving period. The topological phase transitions are also shown to be detectable through studies of transmission properties in the setting of coupled ring resonators. Second, gain and loss are found to induce singularities in the Floquet spectral, around which anomalous transmissions at flat quasienergy bands are predicted. These discoveries not only enhanced our understanding of topological matter and phase transitions in driven non-Hermitian systems, but also promoted their experimental realizations in optical and acoustic settings.

physics.app-ph↗

arXiv2024

Topological phases of commensurate or incommensurate non-Hermitian Su-Schrieffer-Heeger lattices

We theoretically investigate topological features of a one-dimensional Su-Schrieffer-Heeger lattice with modulating non-Hermitian on-site potentials containing four sublattices per unit cell. The lattice can be either commensurate or incommensurate. In the former case, the entire lattice can be mapped by supercells completely. While in the latter case, there are two extra lattice points, thereby making the last cell incomplete. We find that an anti-PT transition occurs at exceptional points of edge states at certain parameters, which does not coincide with the conventional topological phase transition characterized by the Berry phase, provided the imaginary on-site potential is large enough. Interestingly, when the potential exceeds a critical value, edge states appear even in the regime with a trivial Berry phase. To characterize these novel edge states we present topological invariants associated with the system's parity. Finally, we analyze the dynamics for initial states with different spatial distributions, which exhibit distinct dynamics for the commensurate and incommensurate cases, depending on the imaginary part of edge state energy.

cond-mat.mes-hall↗

arXiv2024

Kinked linear response from non-Hermitian cold-atom pumping

It is well known that non-Hermitian, non-reciprocal systems may harbor exponentially localized skin modes. However, in this work, we find that, generically, non-Hermiticity gives rise to abrupt and prominent kinks in the semi-classical wave packet trajectories of quantum gases, despite the absence of sudden physical impulses. This physically stems from a hitherto underappreciated intrinsic non-locality from non-Hermitian pumping, even if all physical couplings are local, thereby resulting in enigmatic singularities in the band structure that lead to discontinuous band geometry and Berry curvature. Specifically, we focus on the realization of the kinked response in an ultracold atomic setup. For a concrete experimental demonstration, we propose an ultracold atomic setup in a two-dimensional optical lattice with laser-induced loss such that response kinks can be observed without fine-tuning in the physical atomic cloud dynamics. Our results showcase unique non-monotonic behavior from non-Hermitian pumping beyond the non-Hermitian skin effect and suggest new avenues for investigating non-Hermitian dynamics on ultracold atomic platforms.

cond-mat.quant-gas↗

arXiv2024

Topological Non-Hermitian skin effect

This article reviews recent developments in the non-Hermitian skin effect (NHSE), particularly on its rich interplay with topology. The review starts off with a pedagogical introduction on the modified bulk-boundary correspondence, the synergy and hybridization of NHSE and band topology in higher dimensions, as well as, the associated topology on the complex energy plane such as spectral winding topology and spectral graph topology. Following which, emerging topics are introduced such as non-Hermitian criticality, dynamical NHSE phenomena, and the manifestation of NHSE beyond the traditional linear non-interacting crystal lattices, particularly its interplay with quantum many-body interactions. Finally, we survey the recent demonstrations and experimental proposals of NHSE.

cond-mat.mes-hall↗

arXiv2024

Activating non-Hermitian skin modes by parity-time symmetry breaking

Parity-time ($\mathcal{PT}$) symmetry is a cornerstone of non-Hermitian physics as it ensures real energies for stable experimental realization of non-Hermitian phenomena. In this work, we propose $\mathcal{PT}$ symmetry as a paradigm for designing rich families of higher-dimensional non-Hermitian states with unique bulk, surface, hinge or corner dynamics. Through systematically breaking or restoring $\mathcal{PT}$ symmetry in different sectors of a system, we can selectively activate or manipulate the non-Hermitian skin effect (NHSE) in both the bulk and topological boundary states. Some fascinating phenomena include the directional toggling of the NHSE, and the flow of boundary states without chiral or dynamical pumping, developed from selective boundary NHSE. Our results extend richly into 3D or higher, with more sophisticated interplay with selective bulk and boundary NHSE and charge-parity ($\mathcal{CP}$) symmetry. Based on non-interacting lattices, $\mathcal{PT}$-activated NHSEs can be observed in various optical, photonic, electric and quantum platforms that admit gain/loss and non-reciprocity.

cond-mat.mes-hall↗

arXiv2024

Observation of scale-free localized states induced by non-Hermitian defects

Wave localization is a fundamental phenomenon that appears universally in both natural materials and artificial structures and plays a crucial role in understanding the various physical properties of a system. Usually, a localized state has an exponential profile with a localization length independent of the system size. Here, we experimentally demonstrate a new class of localized states called scale-free localized states, which has an unfixed localization length scaling linearly with the system size. Using circuit lattices, we observe that a non-Hermitian defect added to a Hermitian lattice induces an extensive number of states with scale-free localization. Furthermore, we demonstrate that, in a lattice with a parity-time-symmetric non-Hermitian defect, the scale-free localization emerges because of spontaneous parity-time symmetry breaking. Our results uncover a new type of localized states and extend the study of defect physics to the non-Hermitian regime.

cond-mat.mes-hall↗

arXiv2023

Topologically compatible non-Hermitian skin effect

The bulk-boundary correspondence (BBC) relates in-gap boundary modes to bulk topological invariants. In certain non-Hermitian topological systems, conventional BBC becomes invalid in the presence of the non-Hermitian skin effect (NHSE), which manifests as distinct energy spectra under the periodic and open boundary conditions and massive eigenstate localization at boundaries. In this work, we introduce a scheme to induce NHSE without breaking conventional BBC, dubbed as the topologically compatible NHSE (TC-NHSE). In a general one dimensional two-band model, we unveil two types of TC-NHSE that do not alter topological phase transition points under any circumstance or only in a certain parameter regime, respectively. Extending our model into two dimension, we find that TC-NHSE can be selectively compatible to different sets of Weyl points between different bands of the resultant semimetallic system, turning some of them into bulk Fermi arcs while keeping the rest unchanged. Our work hence helps clarify the intricate interplay between topology and NHSE in non-Hermitian systems, and provides a versatile approach for designing non-Hermitian topological systems where topological properties and NHSE do not interfere each other.

cond-mat.mes-hall↗

arXiv2023

A brief review of hybrid skin-topological effect

The finding of non-Hermitian skin effect has revolutionized our understanding of non-Hermitian topological phases, where the usual bulk-boundary correspondence is broken and new topological phases specific to non-Hermitian system are uncovered. Hybrid skin-topological effect (HSTE) is a class of newly discovered non-Hermitian topological states that simultaneously supports skin-localized topological edge states and extended bulk states. Here we provide a brief review of HSTE, starting from different mechanics that have been used to realize HSTE, including non-reciprocal couplings, onsite gain/loss, and non-Euclidean lattice geometries. We also review some theoretical developments closely related to the HSTE, including the concept of higher-order non-Hermitian skin effect, parity-time symmetry engineering, and non-Hermitian chiral skin effect. Finally, we summarize recent experimental exploration of HSTE, including its realization in electric circuits systems, non-Hermitian photonic crystals, and active matter systems. We hope this review can make the concept of hybrid-skin effect clearer and inspire new finding of non-Hermitian topological states in higher dimensional systems.

cond-mat.mes-hall↗

arXiv2023

Extrinsic higher-order topological corner states in AB-stacked transition-metal dichalcogenides

Higher-order topological insulators (HOTIs) are a novel type of topological phases which supports $d$-dimensional topological boundary states in $D$-dimensional systems with $D-d>1$. In this work, we theoretically predict that interlayer couplings in AB-stacked bilayer transition-metal dichalcogenides (TMDs) lead to the emergence of extrinsic second-order topological phases, where corner states are induced by the band inversion of zigzag edge bands. We find that the systems feature a quantized multiband Berry phase defined for a zigzag nanoribbon geometry, unveiling the nontrivial topological properties of its two zigzag edges. With detailed investigation into the bilayer TMDs under different geometries, we find two types of boundary-obstructed corner states arising from different corner terminations of either the same type of or heterogeneous zigzag edges. The topological nature of these corner states and their degeneracy is further analyzed with both the crystalline symmetries of different geometries, and a topological phase transition of the Berry phase induced by a layer-dependent onsite energy.

cond-mat.mes-hall↗

arXiv2023

Occupation-dependent particle separation in one-dimensional non-Hermitian lattices

We unveil an exotic phenomenon arising from the intricate interplay between non-Hermiticity and many-body physics, namely an occupation-dependent particle separation for hardcore bosons in a one-dimensional lattice driven by uni-directional non-Hermitian pumping. Taking hardcore bosons as an example, we find that a pair of particles occupying the same unit cell exhibit an opposite non-Hermitian pumping direction to that of unpaired ones occupying different unit cells. By turning on an intracell interaction, many-body eigenstates split in their real energies, forming separable clusters in the complex energy plane with either left-, right-, or bipolar-types of non-Hermitian skin effect (NHSE). The dependency of skin accumulating directions on particle occupation is further justified with local sublattice correlation and entanglement entropy of many-body eigenstates. Dynamically, this occupation-dependent NHSE manifests as uni- or bi-directional pumping for many-body initial states, allowing for spatially separating paired and unpaired particles. Similar phenomena also apply to fermionic systems, unveiling the possibility of designing and exploring novel non-Hermitian phases originated from particle non-conservation in subsystems (e.g., orbitals, sublattices, or spin species) and their spatial configurations.

cond-mat.quant-gas↗

arXiv2023

Geometry-dependent skin effect and anisotropic Bloch oscillations in a non-Hermitian optical lattice

The interplay between the non-Hermiticity and dimensionality gives rise to exotic characteristics in higher dimensions, with one representative phenomenon known as the geometry-dependent skin effect (GDSE), which refers to that the localization of extensive eigenstates depends on the system's geometry under open boundary conditions. In this paper, we demonstrate the emergence of GDSE in a two-dimensional $sp$ optical ladder lattice with on-site atom loss, which can be manifested by anisotropic dynamics of Bloch oscillations in the bulk of the system. By applying a static force in different directions, the wave-packet dynamics retrieve the complex energy spectra with either nonzero or zero spectral winding number, indicating the presence or absence of skin accumulation in the corresponding directions, respectively. Our results reveal that the GDSE has an intrinsic anisotropic bulk dynamics independent of boundary conditions, and offer its realization and detection in quantum systems.

quant-ph↗

arXiv2022

Topological classification of Higher-order topological phases with nested band inversion surfaces

Higher-order topological phases (HOTPs) hold gapped bulk bands and topological boundary states localized in boundaries with codimension higher than one. In this paper, we provide a unified construction and topological characterization of HOTPs for the full Altland-Zirnbauer tenfold symmetry classes, based on a method known as nested band inversion surfaces (BISs). Specifically, HOTPs built on this method are decomposed into a series of subsystems, and higher-order topological boundary states emerges from the interplay of their first-order topology. Our analysis begins with a general discussion of HOTPs in continuous Hamiltonians for each symmetry class, then moves on to several lattice examples illustrating the topological characterization based on the nested-BIS method. Despite the example minimal models possessing several spatial symmetries, our method does not rely on any spatial symmetry, and can be easily extended into arbitrary orders of topology in dimensions. Furthermore, we extend our discussion to systems with asymmetric boundary states induced by two different mechanisms, namely, crossed BISs that break a $\mathcal{C}_4$ rotation symmetry, and non-Clifford operators that break certain chiral-mirror symmetries of the minimal models.

cond-mat.mes-hall↗

arXiv2022

Non-Hermitian boundary spectral winding

Spectral winding of complex eigenenergies represents a topological aspect unique in non-Hermitian systems, which vanishes in one-dimensional (1D) systems under the open boundary conditions (OBC). In this work, we discover a boundary spectral winding in two-dimensional non-Hermitian systems under the OBC, originating from the interplay between Hermitian boundary localization and non-Hermitian non-reciprocal pumping. Such a nontrivial boundary topology is demonstrated in a non-Hermitian breathing Kagome model with a triangle geometry, whose 1D boundary mimics a 1D non-Hermitian system under the periodic boundary conditions with nontrivial spectral winding. In a trapezoidal geometry, such a boundary spectral winding can even co-exist with corner accumulation of edge states, instead of extended ones along 1D boundary of a triangle geometry. An OBC type of hybrid skin-topological effect may also emerge in a trapezoidal geometry, provided the boundary spectral winding completely vanishes. By studying the Green's function, we unveil that the boundary spectral winding can be detected from a topological response of the system to a local driving field, offering a realistic method to extract the nontrivial boundary topology for experimental studies.

cond-mat.mes-hall↗

arXiv2022

Tunable symmetry-protected higher-order topological states with fermionic atoms in bilayer optical lattices

Higher-order topological states that possess gapped bulk energy bands and exotic topologically protected boundary states with at least two dimension lower than the bulk have significantly opened a new perspective for understanding of topological quantum matters. Here, we propose to generate two-dimensional topological boundary states for implementing synthetic magnetic flux of ultracold atoms trapped in bilayer optical lattices, which includes Chern insulator, Dirac semimetals, and second-order topological phase (SOTP) by the interplay of the two-photon detuning and effective Zeeman shift. These observed topological phases can be well characterized by the energy gap of bulk, Wilson loop spectra, and the spin textures at the higher symmetric points of system. We show that the SOTP exhibits a pair of $0$D boundary states. While the phases of Dirac semimetals and Chern insulator support the conventional $1$D boundary states due to the principle of bulk-boundary correspondence. Strikingly, the emerged boundary states for Dirac semimetals and SOTP are topologically protected by $\cal P T$-symmetry and chiral-mirror symmetry ($\mathcal{\widetilde{M}}_α$), respectively. In particular, the location of $0$D corner states for SOTP which are associated with existing $\mathcal{\widetilde{M}}_α$-symmetry can be highly manipulated by tuning magnetic flux. Our scheme herein provides a platform for emerging exotic topological boundary states, which may facilitate the study of higher-order topological phases in ultracold atomic gases.

cond-mat.quant-gas↗

arXiv2022

Anomalous Floquet non-Hermitian skin effect in a ring resonator lattice

We present a one-dimensional coupled ring resonator lattice exhibiting a variant of the non- Hermitian skin effect (NHSE) that we call the anomalous Floquet NHSE. Unlike existing approaches to achieving the NHSE by engineering gain and loss on different ring segments, our design uses fixed on-site gain or loss in each ring. The anomalous Floquet NHSE is marked by the existence of skin modes at every value of the Floquet quasienergy, allowing for broadband asymmetric transmission. Varying the gain/loss induces a non-Hermitian topological phase transition, reversing the localization direction of the skin modes. An experimental implementation in an acoustic lattice yields good agreement with theoretical predictions, with a very broad relative bandwidth of around 40%.

cond-mat.mes-hall↗

arXiv2022

Designing non-Hermitian real spectra through electrostatics

Non-hermiticity presents a vast newly opened territory that harbors new physics and applications such as lasing and sensing. However, only non-Hermitian systems with real eigenenergies are stable, and great efforts have been devoted in designing them through enforcing parity-time (PT) symmetry. In this work, we exploit a lesser-known dynamical mechanism for enforcing real-spectra, and develop a comprehensive and versatile approach for designing new classes of parent Hamiltonians with real spectra. Our design approach is based on a novel electrostatics analogy for modified non-Hermitian bulk-boundary correspondence, where electrostatic charge corresponds to density of states and electric fields correspond to complex spectral flow. As such, Hamiltonians of any desired spectra and state localization profile can be reverse-engineered, particularly those without any guiding symmetry principles. By recasting the diagonalization of non-Hermitian Hamiltonians as a Poisson boundary value problem, our electrostatics analogy also transcends the gain/loss-induced compounding of floating-point errors in traditional numerical methods, thereby allowing access to far larger system sizes.

cond-mat.other↗

arXiv2022

Edge magnetism in transition metal dichalcogenide nanoribbons: Mean field theory and determinant quantum Monte Carlo

Edge magnetism in zigzag transition metal dichalcogenide nanoribbons is studied using a three-band tight-binding model with local electron-electron interactions. Both mean field theory and the unbiased, numerically exact determinant quantum Monte Carlo method are applied. Depending on the edge filling, mean field theory predicts different phases: gapped spin dimer and antiferromagnetic phases appear for two specific fillings, with a tendency towards metallic edge-ferromagnetism away from those fillings. Determinant quantum Monte Carlo simulations confirm the stability of the antiferromagnetic gapped phase at the same edge filling as mean field theory, despite being sign-problematic for other fillings. The obtained results point to edge filling as yet another key ingredient to understand the observed magnetism in nanosheets. Moreover, the filling dependent edge magnetism gives rise to spin-polarized edge currents in zigzag nanoribbons which could be tuned through a back gate voltage, with possible applications to spintronics.

cond-mat.str-el↗