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Shujie Cheng

Publications and source records attributed to Shujie Cheng.

At least 19 recordsLinked to original sources
arXiv2026

Unbound States and Mixed Bound--Unbound Phases in Near-Infinitely Deep Potentials

We investigate the robustness of unbound states in one-dimensional quasiperiodic models with near-infinitely deep potentials. By constructing a deeper extension of the Liu-Xia model and combining inverse participation ratio (IPR) calculations with Lyapunov-exponent analysis based on Avila's global theory, we show that increasing the potential depth does not eliminate unbound states. Instead, it shifts and narrows their energy window to $-2t-V<E<2t-V$. We further extend the analysis to non-Hermitian quasiperiodic potentials with gain and loss. In these systems, unbound states survive within analytically determined real-energy intervals, but they no longer occupy the whole interval uniformly; rather, they coexist with bound states and form a mixed bound-unbound phase. The corresponding boundaries between the mixed region and the pure bound-state regions are obtained exactly from the Lyapunov exponent. These results demonstrate that unbound states in extreme quasiperiodic potentials are controlled not only by the potential depth but also by the spectral and localization structures induced by non-Hermiticity.

cond-mat.dis-nn↗
arXiv2026

Thermodynamic modes of a quasiperiodic mobility-edge system in a quantum Otto cycle

We investigate thermodynamic operation of a quasiperiodic lattice with an exact mobility edge, described by the Biddle--Das Sarma model. We use this model as the working medium of a quantum Otto cycle and map its operating mode as a function of the hopping-range parameter $p$, the initial and final potential strengths $V_i$ and $V_f$, and two idealized protocols for the isolated strokes. In a near-adiabatic (state-frozen) protocol, where the density matrix is approximately unchanged during the isolated strokes, the cycle supports only two modes: a \emph{heater} and an \emph{accelerator}. In an adiabatic protocol, where level populations are preserved while the spectrum is deformed, two additional modes appear: a \emph{heat engine} and a \emph{refrigerator}. Our results show that mobility-edge systems can realize multiple thermodynamic functions within a single platform and provide guidance for switching between modes by tuning $p$, $V_i$, and $V_f$.

cond-mat.dis-nn↗
arXiv2026

Wigner distribution, Wigner entropy and Quantum Refrigerator of a One-Dimensional Off-diagonal Quasicrystal

We investigate an off-diagonal quasicrystal featuring simultaneous off-diagonal and diagonal quasiperiodic modulations. By analyzing the fractal dimension, we map out the delocalization-localization phase diagram. We demonstrate that delocalized and localized states can be distinguished via the Wigner distribution, while extended, critical, and localized phases are separated using the Wigner entropy. Furthermore, we explore the quantum thermodynamic properties, revealing that localized states facilitate the emergence of a quantum heater mode, alongside the appearance of a refrigerator mode. These findings enhance our understanding of localization phenomena and expand the thermodynamic applications of quasiperiodic systems.

cond-mat.stat-mech↗
arXiv2025

High-Winding-Number Zero-Energy Edge States in Rhombohedral-Stacked Su-Schrieffer-Heeger Multilayers

We study the topological properties of rhombohedral-stacked N-layer Su-Schrieffer-Heeger networks with interlayer coupling. We find that these systems exhibit $2N$-fold degenerate zero-energy edge states with winding number $W=N$, providing a direct route to high-winding-number topological phases where $W$ equals the layer number. Using effective Hamiltonian theory and Zak phase calculations, we demonstrate that the winding number scales linearly with $N$ through a layer-by-layer topological amplification mechanism. We introduce the Wigner entropy as a novel detection method for these edge states, showing that topological boundary states exhibit significantly enhanced Wigner entropy compared to bulk states. Our results establish rhombohedral stacking as a systematic approach for engineering high-winding-number topological insulators with potential applications in quantum information processing.

cond-mat.dis-nn↗
arXiv2025

Fate and origin of the quantum Otto heat engine based on the dissipative Dicke-Hubbard model

The Dicke-Hubbard model, describing an ensemble of interacting atoms in a cavity, provides a rich platform for exploring collective quantum phenomena. However, its potential for quantum thermodynamic applications remains largely uncharted. Here, we study a quantum Otto heat engine whose working substance is a system governed by the Dicke-Hubbard Hamiltonian. Through the research on steady-state superradiance phase transitions, it is demonstrated that the steady-state synergistic mechanism under high and low temperature environments is the reason for the emergence of high-performance heat engines. By analyzing the influences of atom-light coupling strength, inter-cavity hopping strength and atom number on the working modes of quantum Otto cycle, it is clarified that the effective working regions of each working mode. This work has established a close connection between superradiance phase transition and the quantum thermodynamic applications. It not only deepens our understanding of the energy conversion mechanism in non-equilibrium quantum thermodynamics but also lays a theoretical foundation for the future experimental design of high-performance quantum Otto heat engines.

cond-mat.quant-gas↗
arXiv2025

Quantum Mpemba effect in quasiperiodic systems

We study a one-dimensional quasiperiodic tight-binding model with simultaneous off-diagonal (hopping) and diagonal (onsite) modulations. Using the inverse participation ratio and the wave-packet centroid, we construct localization-delocalization phase diagrams for both equilibrium and nonequilibrium steady states. We analyze the robustness of initial-state properties under dissipation and characterize dissipation-induced localization-delocalization transitions (and their reversals) in detail. Trace-distance dynamics provide evidence for a quantum Mpemba effect: states prepared farther from the steady state can relax faster than states initialized closer to it. We propose a starting-line hypothesis that explains the presence or absence of this effect across parameter regimes. These results advance the understanding of steady-state phase transitions and relaxation dynamics in dissipatively driven quasiperiodic systems.

cond-mat.dis-nn↗
arXiv2025

Wigner distribution, Wigner entropy, and Anomalous Transport of a Generalized Aubry-Andr\'{e} model

We investigate generalized Aubry-Andr\'{e} models featuring tunable quasidisordered potentials and a mobility edge that separates extended and localized states, with critical states for the mobility edge confirmed through finite-size scaling analysis. Numerical results demonstrate that extended, critical, and localized states can be distinguished via their phase-space representations, particularly the Wigner distribution. The associated Wigner entropy, derived from this distribution, peaks at the critical state, enabling precise localization of the mobility edge. Additionally, wave-packet dynamics reveal anomalous transport behaviors, including superdiffusion and subdiffusion, bridging ballistic transport and the absence of diffusion.

cond-mat.dis-nn↗
arXiv2025

When Homogeneous Systems Meet Dissipation and Disorder

We investigate the localization and topological properties of the non-equilibrium steady state (NESS) in a one-dimensional homogeneous system. Our results demonstrate that, despite the absence of disorder in the initial system, the NESS can exhibit localization under bond dissipation. These dissipation-driven localization and delocalization phenomena are clearly distinguished using Wigner distributions. Furthermore, we find that the initial localization characteristics of the system significantly influence the localization properties of the NESS. Drawing upon the concept of Bose-Einstein condensate broadening in cold-atom experiments, along with experimental data, we systematically characterize the impact of bond dissipation and disorder on the localization and topological properties of the NESS. The phase diagram reveals that the NESS can be topologically non-trivial even when the initial system is topologically trivial, and that the topological triviality of the initial system strengthens the topological non-triviality of the NESS. This work provides new insights into the localization and topological phase transitions in homogeneous systems induced by bond dissipation and disorder.

cond-mat.dis-nn↗
arXiv2024

Long-range hopping in a quasiperiodic potential weakens the non-Hermitian skin effect

In this paper, we investigate a non-Hermitian Aubry-Andr\'e-Harper model characterized by power-law hoppings ($1/s^{a}$) and a quasi-periodic parameter $\beta$, where $a$ denotes the power-law index, $s$ represents the hopping distance, and $\beta$ belongs to the metallic mean family. In the intermediate phases, we find that ergodic states correspond to complex eigenvalues, multifractal states to real eigenvalues, and localized states may exhibit either complex or real eigenvalues. Moreover, both real and complex energy spectra emerge in the localized phase, with real spectra attributed to pseudo-Hermiticity. Under open boundary conditions, our analysis of fractal dimensions and eigenstates reveals that all ergodic states transform into skin states. Furthermore, we demonstrate that long-range hoppings weaken the skin effect, offering another perspective for exploring non-Hermitian skin effects.

cond-mat.dis-nn↗
arXiv2024

Exploring Metallic-Insulating Transition and Thermodynamic Applications of Fibonacci Quasicrystals

Extended and critical states are two common phenomena in Fibonacci quasicrystals. In this paper, we first reveal the difference between the extended phase and the critical phase in the extended-critical Fibonacci quasicrystal from the perspectives of quantum transport and Wigner distribution. The transport conductance indicates that the extended-critical transition resembles a metallic-insulating transition. Moreover, the Wigner distributions show that the Wigner distribution of the extended wave function is localized in the momentum direction of the phase space, while that of the critical wave function is sub-extended in the momentum direction of the phase space. Based on the results of entanglement entropy, the extended-critical transition is a thermodynamic phase transition because it is accompanied by decreasing entropy. We engineer a quantum heat cycle engine with the extended-critical quasicrystal as the working medium, and find that there are rich working modes in the engine, such as quantum accelerator, quantum heater and quantum heat engine. Importantly, the extended quasicrystals are more conducive to the realization of quantum heat engines, while the critical quasicrystals are more conducive to the realization of quantum heaters. Our work is an important step toward exploring the rich thermodynamic applications of Fibonacci quasicrystals.

cond-mat.dis-nn↗
arXiv2024

Phase driven unconventional superradiance phase transition in non-Hermitian cascaded quantum Rabi cavities

This study investigates phase-driven symmetry breaking leading to superradiance phase transitions in cascaded non-Hermitian quantum Rabi cavities. Non-Hermiticity is introduced via the phase coupling $\varphi$ between the atom and the optical field. In the thermodynamic limit of the quantum harmonic oscillator, we analytically derive the superradiance phase boundary, validated by observables. An unconventional quantum phase transition without a Hermitian analogue arises when $|\varphi|=\frac{\pi}{4}$ or $|\varphi|=\frac{3\pi}{4}$, where the phase boundary is uniquely determined by the cavity coupling, at $\mathcal{J}=\frac{1}{2}$, independent of the atom-photon coupling strength $g$. For other $\varphi$, the phase boundary relies on both $\mathcal{J}$ and $g$, similar to the scenario observed in Hermitian systems. Furthermore, we identify phase-driven first- and second-order superradiance phase transitions, focusing on the quantum criticality of the second-order transition by determining the critical exponents and the universality class. The feasibility of experimental realization is also discussed, aiming to inspire further studies on non-Hermitian superradiance quantum phase transitions.

cond-mat.quant-gas↗
arXiv2023

Bulk-edge correspondence for the nonlinear eigenvalues problem of the Haldane model

Recently, there is an interest in studying the bulk-edge correspondence for nonlinear eigenvalues problems in a two-dimensional topological system with spin-orbit coupling. By introducing auxiliary eigenvalues, the nonlinear bulk-edge correspondence was established. In this paper, taking the Haldane model as an example, we address that such a correspondence will appear in two dimensional topological system without spin-orbit coupling. The resulting edge states are characterized by the Chern number of the auxiliary energy band. A full phase diagram containing topological nontrivial phase, topological trivial phase, and metallic phase is obtained. Our work generalizes the study of the bulk-edge correspondence for nonlinear eigenvalue problems in two-dimensional system.

cond-mat.dis-nn↗
arXiv2023

Stable real-energy spectral dynamics with topological transitions and non-Hermitian many-body localization

In this work, the interplay between non-Hermiticity, quasi-disorder, and repulsive interaction is studied for hard-core bosons confined in a one-dimensional optical lattice, where non-Hermiticity is induced by the non-reciprocal hoppings and the on-site gain and loss breaking the time-reversal symmetry. Although the energy spectra of the static system are fully complex, with the evolution of the initial state, the real part of the expectation value of the Hamiltonian under the time-evolved wave function changes stably. By means of the entanglement entropy and its dynamical evolution, as well as the inverse participation ratio, the many-body localization (MBL) is found to play the key role in the stability of the dynamical behavior of the real part of the expectation value, independent of whether the spectrum of the static Hamiltonian is real or complex. In the delocalization phase, the dynamical evolution of the real part of the expectation value is unstable. Meanwhile, the nearest-neighbor level spacings statistics shows the MBL transition accompanied by the transition from the Ginibre distribution to the complex Poisson distribution, different from the one in the time-reversal invariant system. In addition, the dynamical stability of the real part of the energy and the MBL transition can be characterized by the winding number, indicating that the MBL transition and the topological transition occur simultaneously, and the realization of the Hamiltonian is discussed.

cond-mat.dis-nn↗
arXiv2023

Power law hopping of single particles in one-dimensional non-Hermitian quasicrystals

In this paper, a non-Hermitian Aubry-Andr\'e-Harper model with power-law hoppings ($1/s^{a}$) and quasiperiodic parameter $\beta$ is studied, where $a$ is the power-law index, $s$ is the hopping distance, and $\beta$ is a member of the metallic mean family. We find that under the weak non-Hermitian effect, there preserves $P_{\ell=1,2,3,4}$ regimes where the fraction of ergodic eigenstates is $\beta$-dependent as $\beta^{\ell}$L ($L$ is the system size) similar to those in the Hermitian case. However, $P_{\ell}$ regimes are ruined by the strong non-Hermitian effect. Moreover, by analyzing the fractal dimension, we find that there are two types of edges aroused by the power-law index $a$ in the single-particle spectrum, i.e., an ergodic-to-multifractal edge for the long-range hopping case ($a<1$), and an ergodic-to-localized edge for the short-range hopping case ($a>1$). Meanwhile, the existence of these two types of edges is found to be robust against the non-Hermitian effect. By employing the Simon-Spence theory, we analyzed the absence of the localized states for $a<1$. For the short-range hopping case, with the Avila's global theory and the Sarnak method, we consider a specific example with $a=2$ to reveal the presence of the intermediate phase and to analytically locate the intermediate regime and the ergodic-to-multifractal edge, which are self-consistent with the numerically results.

cond-mat.dis-nn↗
arXiv2022

From topological phase to Anderson localization in a two-dimensional quasiperiodic system

In this paper, the influence of the quasidisorder on a two-dimensional system is studied. We find that there exists a topological phase transition accompanied by a transverse Anderson localization. The topological properties are characterized by the band gap, the edge-state spectra, the transport conductance, and the Chern number. The localization transition is clearly demonstrated by the investigations of the partial inverse participation ratio, the average of level spacing ratio, and the fraction dimension. The results reveal the topological nature of the bulk delocalized states. Our work facilitates the understanding on the relationship between the topology and the Anderson localization in two-dimensional disordered systems.

cond-mat.dis-nn↗
arXiv2022

Breakdown of the correspondence between the real-complex and delocalization-localization transitions in non-Hermitian quasicrystals

The correspondence between the real-complex transition in energy and delocalization-localization transition is well-established in a class of Aubry-Andr'e-Harper model with exponential non-Hermitian on-site potentials. In this paper, we study a generalized Aubry-Andr'e model with off-diagonal modulation and non-Hermitian on-site potential. We find that, when there exists an incommensurate off-diagonal modulation, the correspondence breaks down, although the extended phase is maintained in a wide parameter range of the strengths of the on-site potential and the off-diagonal hoppings. An additional intermediate phase with a non-Hermitian mobility edge emerges when the off-diagonal hoppings become commensurate. This phase is characterized by the real and complex sections of the energy spectrum corresponding to the extended and localized states. In this case, the aforementioned correspondence reappears due to the recovery of the PT-symmetry.

cond-mat.dis-nn↗
arXiv2022

Topological Floquet-bands in a circularly shaken dice lattice

The hoppings of non-interacting particles in the optical dice lattice result in the gapless dispersions in the band structure formed by the three lowest minibands. In our research, we find that once a periodic driving force is applied to this optical dice lattice, the original spectral characteristics could be changed, forming three gapped quasi-energy bands in the quasi-energy Brillouin zone. The topological phase diagram containing the Chern number of the lowest quasi-energy band shows that when the hopping strengths of the nearest-neighboring hoppings are isotropic, the system persists in the topologically non-trivial phases with Chern number $C=2$ within a wide range of the driving strength. Accompanied by the anisotropic nearest-neighboring hopping strengths, a topological phase transition occurs, making Chern number change from $C=2$ to $C=1$. This transition is further verified by our analytical method. Our theoretical work implies that it is feasible to realize the non-trivially topological characteristics of optical dice lattices by applying the periodic shaking, and that topological phase transition can be observed by independently tuning the strength of a type of nearest-neighbor hopping.

cond-mat.quant-gas↗