arXiv subjects

Shan-Zhong Li

Publications and source records attributed to Shan-Zhong Li.

17 recordsLinked to original sources

arXiv2026

Nonlocal Magic across the Many-Body Localization Crossover

Nonlocal magic quantifies the minimum nonstabilizerness attainable under independent local unitary transformations on the two subsystems. Here, we use min-relative nonlocal magic (NLM) to characterize the crossover from ergodicity to many-body localization (MBL) in the random-field XXZ chain. Unlike entanglement entropy, NLM probes how entanglement is organized through the distance of the Schmidt spectrum from dyadic-flat stabilizer spectra. From weak to intermediate disorder, NLM evolves from an $O(1)$ Haar-like value into a size-enhanced dome, while entanglement remains volume-law, revealing a spectral reorganization not visible in the entropy. Deep in the MBL regime, a two-level cut-hybridization model captures the nearly binary Schmidt spectrum and explains why the mean and median NLM decay approximately as $W^{-1}$ and $W^{-2}$, respectively. Following a product-state quench, NLM overshoots and relaxes in the ergodic regime, whereas at strong disorder it grows slowly and approximately logarithmically. These results show that NLM resolves Schmidt-spectrum structure not visible in the entanglement entropy and provides a complementary probe of ergodicity breaking.

cond-mat.dis-nn↗

arXiv2026

Nonlinear Photonic Tripartite Phase

Anderson localization is usually understood as a transition between extended and localized phases, with criticality confined to a single mobility edge. Recent advances predict that quasiperiodic systems can instead host a finite critical window bounded by mobility edges, in which localized, critical and extended states coexist. Yet both the experimental realization of this regime and whether interactions can provide controlled access to it remain unknown. Here, we realize such a tripartite phase in a nonlinear quasiperiodic photonic lattice and show that Kerr nonlinearity, acting as an effective interaction, enables state-selective access to the critical window. By tracking wavepacket dynamics, we distinguish localized, critical and extended transport regimes and uncover a state-selective response: rather than simply reinforcing localization through self-trapping, weak nonlinearity drives low-energy localized states into the critical window, whereas stronger nonlinearity restores localization. By contrast, critical, extended and high-energy localized states evolve monotonically towards self-trapped behaviour. Our results reveal a state-selective mechanism by which interactions provide controlled access to a pre-existing critical window in quasiperiodic systems.

cond-mat.mes-hall↗

arXiv2025

Emergent topological re-entrant phase transition in a generalized quasiperiodic modulated Su-Schrieffer-Heeger model

We study the topological properties of the one-dimensional generalized quasiperiodic modulated Su-Schrieffer-Heeger model. The results reveal that topological re-entrant phase transition emerges. Through the analysis of a real-space winding number , we divide the emergent topological re-entrant phase transitions into two types. The first is the re-entrant phase transition from the traditional topological insulator phase into the topological Anderson insulator phase, and the second is the re-entrant phenomenon from one topological Anderson insulator phase into another topological Anderson insulator phase. These two types of re-entrant phase transition correspond to bounded and unbounded cases of quasiperiodic modulation, respectively. Furthermore, we verify the above topological re-entrant phase transitions by analyzing the Lyapunov exponent and bulk gap. Since Su-Schrieffer-Heeger models have been realized in various artificial systems (such as cold atoms, optical waveguide arrays, ion traps, Rydberg atom arrays, etc.), the two types of topological re-entrant phase transition predicted in this paper are expected to be realized in the near future.

cond-mat.mes-hall↗

arXiv2025

Anderson-skin dualism: A boundary-dependent effect in non-Hermitian disordered coupled systems

We report a novel localization phenomenon that emerges in non-Hermitian and quasiperiodic coupled systems, which we dub ``Anderson-Skin (AS) dualism". The emergence of AS dualism is due to the fact that non-Hermitian topological systems provide non-trivial topological transport channels for disordered systems, causing the originally localized Anderson modes to transform into skin modes, i.e., the localized states within the point gap regions have dual characteristics of localization under periodic boundary condition (PBC) and skin effects under open boundary conditions (OBC). As an example, we analytically prove the 1D AS dualism through the transfer matrix method. Moreover, by discussing many-body interacting systems, we confirm that AS dualism is universal.

cond-mat.dis-nn↗

arXiv2025

Multifractal-enriched mobility edges and emergent quantum phases in Rydberg atomic arrays

Anderson localization describes disorder-induced phase transitions, distinguishing between localized and extended states. In quasiperiodic systems, a third multifractal state emerges, characterized by unique energy and wave functions. However, the corresponding multifractal-enriched mobility edges and three-state-coexisting quantum phases have yet to be experimentally detected. In this work, we propose exactly-solvable one-dimensional quasiperiodic lattice models that simultaneously host three-state-coexisting quantum phases, with their phase boundaries analytically derived via Avila's global theorem. Furthermore, we propose experimental protocols via Rydberg atom arrays to realize these states. Notably, we demonstrate a spectroscopic technique capable of measuring inverse participation ratios across real-space and dual-space domains, enabling simultaneous characterization of localized, extended, and multifractal quantum phases in systems with up to tens of qubits. Our work opens new avenues for the experimental exploration of Anderson localization and multifractal states in artificial quantum systems.

cond-mat.dis-nn↗

arXiv2025

Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice

We propose a geometric series modulated non-Hermitian quasiperiodic lattice model, and explore its localization and topological properties. The results show that with the ever-increasing summation terms of the geometric series, multiple mobility edges and non-Hermitian point gaps with high winding number can be induced in the system. The point gap spectrum of the system has a multi-loop nested structure in the complex plane, resulting in a high winding number. In addition, we analyze the limit case of summation of infinite terms. The results show that the mobility edges merge together as only one mobility edge when summation terms are pushed to the limit. Meanwhile, the corresponding point gaps are merged into a ring with winding number equal to one. Through Avila's global theory, we give an analytical expression for mobility edges in the limit of infinite summation, reconfirming that mobility edges and point gaps do merge and will result in a winding number that is indeed equal to one.

cond-mat.dis-nn↗

arXiv2025

Emergent chiral toplogical point gaps in a non-Hermitian quasiperiodic Su-Schrieffer-Heeger model

We study a quasiperiodic Su-Schrieffer-Heeger lattice with staggered on-site gain-loss. The results reveal that on-site staggered gain-loss can effectively induce non-Hermitian topological gap without introducing imaginary phase. Further analysis exhibits that five different processes of topological phase transitions, including topological re-entrant phenomena, with the gain-loss intensity increasing. In addition, through the analysis of inverse participation ratios, normalized participation ratios, winding number and other indicators, we find that topological phase transitions occur synchronically with localized phase transitions. Finally, by investigating the properties of dual space eigenfunction, we reveal that the non-Hermitian topological point gaps predicted in this paper are chiral point gaps, which have a pair of skin modes along opposite directions simultaneously.

cond-mat.dis-nn↗

arXiv2025

Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential

In this study, we investigate the problem of Anderson localization in a one-dimensional flat band lattice with a non-Hermitian quasiperiodic on-site potential. First of all, we discuss the influences of non-Hermitian potentials on the existence of critical states. Our findings show that, unlike in Hermitian cases, the non-Hermiticity of the potential leads to the disappearance of critical states and critical regions. Furthermore, we are able to accurately determine the Lyapunov exponents and the mobility edges. Our results reveal that the mobility edges form mobility lines and mobility rings in the complex energy plane. Within the mobility rings, the eigenstates are extended, while the localized states are located outside the mobility rings. For mobility line cases, only when the eigenenergies lie on the mobility lines, their corresponding eigenstates are extended states.Finally, as the energy approaches the mobility edges, we observe that, differently from Hermitian cases, here the critical index of the localization length is not a constant, but rather varies depending on the positions of the mobility edges.

cond-mat.dis-nn↗

arXiv2025

Emergent extended states in an unbounded quasiperiodic lattice

Previous studies have established that quasiperiodic lattice models with unbounded potentials can exhibit localized and multifractal states, yet preclude the existence of extended states. In this work, we introduce a quasiperiodic system that incorporates both unbounded potentials and unbounded hopping amplitudes, where extended states emerge as a direct consequence of the unbounded hopping terms overcoming the localization constraints imposed by the unbounded potential, thereby facilitating enhanced particle transport. By using Avila's global theory, we derive analytical expressions for the phase boundaries, with exact results aligning closely with numerical simulations.Intriguingly, we uncover a hidden self-duality in the proposed model by establishing a mapping to the Aubry-André model, revealing a profound structural connection between these systems.

cond-mat.dis-nn↗

arXiv2025

Fate of pseudo mobility-edge and multiple states in non-Hermitian Wannier-Stark lattice

The interaction between non-reciprocity and disorder-free localization has emerged as a fascinating open question. Here, we explore the effects of pseudo mobility edges (MEs) along with different types of eigenstates in a one-dimensional (1D) lattice subjected to a non-reciprocal finite-height Wannier-Stark ladder. Utilizing the transfer matrix method, we analytically investigate the pseudo mobility edges under non-reciprocity, which accurately describe the boundary between ergodic and non-ergodic states. The ergodic states, under nonreciprocity, form topological point gaps in the complex plane, with the corresponding eigenstates localized at the boundaries. The localization of mixed states induced by the skin effect and Wannier-Stark ladder is further amplified under non-reciprocity. Through similarity transformations, the fate of multiple eigenstates under non-reciprocal transitions can be captured. Finally, we use wave packet dynamics as a means to detect these emerging states. Our findings broaden the understanding of disorder-free localization in non-Hermitian systems.

cond-mat.dis-nn↗

arXiv2024

Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals

The Lyapunov exponent, serving as an indicator of the localized state, is commonly utilized to identify localization transitions in disordered systems. In non-Hermitian quasicrystals, the non-Hermitian effect induced by non-reciprocal hopping can lead to the manifestation of two distinct Lyapunov exponents on opposite sides of the localization center. Building on this observation, we here introduce a comprehensive approach for examining the localization characteristics and mobility edges of non-reciprocal quasicrystals, referred to as asymmetric transfer matrix analysis. We demonstrate the application of this method to three specific scenarios: the non-reciprocal Aubry-André model, the non-reciprocal off-diagonal Aubry-André model, and the non-reciprocal mosaic quasicrystals. This work may contribute valuable insights to the investigation of non-Hermitian quasicrystal and disordered systems.

cond-mat.dis-nn↗

arXiv2024

Emergent strength-dependent scale-free mobility edge in a non-reciprocal long-range Aubry-André-Harper model

We investigate the properties of mobility edge in an Aubry-André-Harper model with non-reciprocal long-range hopping. The results reveal that there can be a new type of mobility edge featuring both strength-dependent and scale-free properties. By calculating the fractal dimension, we find that the positions of mobility edges are robust to the strength of non-reciprocal long-range hopping. Furthermore, through scale analysis of the observables such as fractal dimension, eigenenergy and eigenstate, etc., we show that four different specific mobility edges can be observed in the system. This paper extends the family tree of mobility edges and hopefully it will shed more light on the related theory and experiment.

cond-mat.dis-nn↗

arXiv2024

Ring Structure in the Complex Plane: A Fingerprint of non-Hermitian Mobility Edge

By Avila's global theory, we analytically reveal that the non-Hermitian mobility edge will take on a ring structure in the complex plane, which we name as "mobility ring". The universality of mobility ring has been checked and supported by the Hermitian limit, $PT$-symmetry protection and without $PT$-symmetry cases. Further, we study the evolution of mobility ring versus quasiperiodic strength, and find that in the non-Hermitian system, there will appear multiple mobility ring structures. With cross-reference to the multiple mobility edges in Hermitian case, we give the expression of the maximum number of mobility rings. Finally, by comparing the results of Avila's global theorem and self-duality method, we show that self-duality relation has its own limitations in calculating the critical point in non-Hermitian systems. As we know, the general non-Hermitian system has a complex spectrum, which determines that the non-Hermitian mobility edge can but exhibit a ring structure in the complex plane.

cond-mat.dis-nn↗

arXiv2024

Emergent entanglement phase transitions in non-Hermitian Aubry-André-Harper chains

We investigate the entanglement dynamics of the non-Hermitian Aubry-André-Harper (AAH) chain. The results reveal that by increasing quasiperiodic strength, a phase transition occurs from the area law induced by non-Hermitian skin effect to the area law arising from Anderson localization. For the former, the entanglement entropy follows a non-monotonic process, i.e., it increases first, then oscillates, and finally converges to a stable value. While for the latter, the entanglement entropy remains low because the wave function is not expandable in Anderson's localization region. The early-stage behavior of entanglement entropy indicates that the two area-law cases are of different phases. Interestingly, the volume-law behavior emerges at the critical point between these two area-law phases. Our study reveals that the area laws induced by the skin effect and the Anderson localization is two different phases, and that a volume law can emerge at the phase transition point. The understanding of the entanglement phase transition induced by disorder and skin effect is thus deepened.

cond-mat.dis-nn↗

arXiv2023

The multiple re-entrant localization in a phase-shift quasiperiodic chain

Inspired by the recently discovered phenomenon of re-entrant localization (REL) [Roy et al., PRL 126, 106803 (2021)], we propose a new approach to induce REL, i.e., to control the quasiperiodic potential's phase-shift between odd and even sites, as thus the system can be dubbed as a phase-shift AAH model. We then analyze the participation ratios and corresponding scaling behaviors, and the results reveal that multiple re-entrant localization (MREL) phenomenon occurs. Furthermore, by depicting the behavior of extension dynamics, we obtain a whole visualized process of the system entering and re-entering the localized phase multiple times. Finally, we exhibit the distribution of quasiperiodic potential with different phase-shift and quasiperiodic parameter, and show the reason for the occurrence of MREL phenomenon, i.e., the introduction of phase-shift enables a part of eigenstates to escape from the localized phase, thus weakening the ``localizibility'' of the system.

cond-mat.dis-nn↗

arXiv2023

Emergent Recurrent Extension Phase Transition in a Quasiperiodic Chain

We study $p$-wave superconducting quasiperiodic chains with staggered potential. The result shows a counter-intuitive phase transition phenomenon, i.e., recurrent extension phase transition (REPT). By analyzing the participation ration and scaling behavior, we prove the existence of REPT phenomenon, which, in concrete terms, means that the system will repeatedly return from the intermediate phase to the extended phase as the quasiperiodic or staggered strength grows. Furthermore, our finding is also quite different from the traditional understanding of intermediate phase (composed only of the pure extended phase and pure localized phase) in that, the new intermediate phase described here, stemming from the competition between staggered potential and $p$-wave pairing, actually falls into three types by bringing in the critical phase. To be specific, the new intermediate phases are composed of the critical + extended states, the critical + localized states, and the critical + extended + localized states, respectively.

cond-mat.dis-nn↗

arXiv2023

Anderson Localization and Swing Mobility Edge in Curved Spacetime

We construct a quasiperiodic lattice model in curved spacetime to explore the crossover concerning both condensed matter and curved spacetime physics. We study the related Anderson localization and find that the model has a clear boundary of localized-extended phase separation, which leads to a swing mobility edge, i.e., the coexistence of localized, swing and sub-extended phases. The swing mobility edge, first reported here, features the phase-dependent eigenstate, that is, the eigenstate swing between the extended and localized state for differnt phase parameter of the quasiperiodic potential. Furthermore, A novel self-consistent segmentation method is developed to calculate the analytical expression of the critical point of phase separation, and the rich phase diagram is obtained by calculating the fractal dimension and scaling index in multifractal analysis.

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