arXiv subjects

Yan-Qing Zhu

Publications and source records attributed to Yan-Qing Zhu.

At least 19 recordsLinked to original sources

arXiv2026

Probing Tensor Singularities and Their Euler-Class Descendants via Non-Abelian Quantum Geometry Measurement

We report the theoretical prediction and experimental observation of a new class of four-dimensional (4D) tensor singularities and their three-dimensional (3D) Euler-class descendants, protected by chiral and spacetime inversion symmetries on a superconducting circuit platform. The 4D point-like singularity/monopole, characterized by the Dixmier-Douady class of a real bundle gerbe associated with tensor gauge fields, is observed to evolve into a nodal ring carrying an additional first Euler class charge under symmetry-preserving perturbations. Dimensional reduction reveals 3D Euler and Euler curvature dipoles, exhibiting nontrivial Euler topology and a topological sum rule that ensures zero-energy flat bands inherit nontrivial topology even without interactions. Crucially, these high-dimensional degenerate systems are mapped and reconstructed using a hybrid analog-digital protocol designed for non-Abelian quantum geometry measurement within a superconducting qubit array. Our work not only expands the family of topological monopoles but also establishes a robust experimental framework for exploring high-order gauge theory and real-bundle topology across diverse quantum platforms.

quant-ph↗

arXiv2026

Dynamical Signatures of Floquet Topology in Wave Packet Dynamics

Periodically driven quantum systems, known as Floquet systems, provide a versatile platform for engineering novel topological phases absent in static settings. However, dynamically characterizing these non-equilibrium topological invariants remains a challenge. Here, we develop a Floquet perturbation theory in the extended Hilbert space to analytically describe the center-of-mass (CoM) dynamics of a wave packet. When applied to the driven Su-Schrieffer-Heeger model, our theory reveals that the CoM exhibits multi-frequency Zitterbewegung oscillations, whose spectral composition and phase are directly tied to the system's Floquet band structure. Crucially, we find that band inversions at topological phase transitions imprint distinct signatures in the CoM dynamics, including the emergence of low-frequency modes and phase shifts of the oscillatory trajectory. These dynamical signatures offer a practical protocol for detecting Floquet topological invariants, which we demonstrate for both high-frequency and strongly driven regimes. Our work establishes CoM dynamics as a simple and experimentally accessible probe for exploring topological phase transitions in Floquet systems.

quant-ph↗

arXiv2025

Topological Insulators with Hybrid-order Boundary States

We report the discovery of several classes of novel topological insulators (TIs) with hybrid-order boundary states generated from the first-order TIs with additional crystalline symmetries. Unlike the current studies on hybrid-order TIs where different-order topology arises from merging different-order TIs in various energy, {\color{red} these novel TIs exhibit unique properties, featuring a remarkable coexistence of first-order gapless modes and higher-order Fermi arc states}, behaving as a hybrid between the first-order TIs and higher-order topological semimetals within a single bulk gap. Our findings establish a profound connection between these novel $d$-dimensional ($d$D) TIs and ($d-1$)D higher-order TIs (HOTIs), which can be understood as a result of stacking $(d-1)$D HOTIs to $d$D with $d=3,4$, revealing unconventional topological phase transitions by closing the gap in certain first-order boundaries rather than the bulk. The bulk-boundary correspondence between these higher-order Fermi-arcs and bulk topological invariants associated with additional crystalline symmetries is also demonstrated. We then address the conventional topological phase transitions from these novel TIs to nodal-line/nodal-surface semimetal phases, where the gapless phases host new kinds of topological responses. Meanwhile, we present the corresponding topological semimetal phases by stacking these unique TIs. Finally, we discuss potential ways to realize these novel phases in synthetic and real materials, with a particular focus on the feasible implementation in optical lattices using ultracold atoms.

cond-mat.mes-hall↗

arXiv2024

Synthetic spin-orbit coupling for the multispin models in optical lattices

The essential role of synthetic spin-orbit coupling in discovering new topological matter phases with cold atoms is widely acknowledged. However, the engineering of spin-orbit coupling remains unclear for arbitrary-spin models due to the complexity of spin matrices. In this paper, we develop a more general but relatively straightforward method to achieve spin-orbit coupling for multispin models. Our approach hinges on controlling the coupling between distinct pseudo-spins through two intermediary states, resulting in tunneling with spin flips that have direction-dependent strength. The engineered spin-orbit coupling can facilitate topological phase transitions with Chern numbers over 1, a unique characteristic of multispin models compared to spin-1/2 models. By utilizing existing cold atom techniques, our proposed method provides an ideal platform for investigating topological properties related to large Chern numbers.

cond-mat.quant-gas↗

arXiv2024

Synthetic non-Abelian topological charges in ultracold atomic gases

Topological phases associated with non-Abelian charges can exhibit a distinguished bulk-edge correspondence compared with Abelian phases, although elucidating this relationship remains challenging in traditional solid-state systems. In this paper, we propose a theoretical framework for synthesizing non-Abelian quaternion charges in ultracold atomic gases. By designing artificial spin-orbit coupling patterns, the topological edge modes demonstrate a clear correspondence with the band topology determined by various quaternion charges. This paves the way for observing the interface modes whose existence is attributed to the nonconservation multiplication relation, which is fundamental to non-Abelian charges. This scheme can be readily implemented using current ultracold atom techniques, offering a promising approach to explore the intriguing non-Abelian characteristics of the system.

cond-mat.quant-gas↗

arXiv2024

A spectrum-based shortcut method for topological systems

The need for fast and robust quantum state transfer is an essential element in scalable quantum information processing, leading to widespread interest in shortcuts to adiabaticity for speeding up adiabatic quantum protocols. However, shortcuts to adiabaticity for systems with more than a few levels is occasionally challenging to compute in theory and frequently difficult to implement in experiments. In this work, we develop a protocol for constructing shortcuts to adiabaticity through the multi-state Landau-Zener approach and a stricter adiabatic condition. Importantly, our protocol only requires a few pieces of information about the energy spectrum and just adjusts the evolutionary rate of the system. It means that our protocol has broad applicability to theoretical models and does not require increasing the difficulty of the experiment. As examples, we apply our protocol to state transfer in the two-level Landau-Zener model, the non-Hermitian Su-Schrieffer-Heeger (SSH) model and the topological Thouless pump model and find that it can speed up the manipulation speed while remaining robust to Hamiltonian errors. Furthermore, based on the experimental friendliness of our findings, it can potentially be extended to many-body systems, dissipation cases, or Floquet processes. Overall, the proposed shortcut protocol offers a promising avenue for enhancing the efficiency and reliability of quantum state transfer protocols.

quant-ph↗

arXiv2024

Emergent Non-Abelian Thouless Pumping Induced by the Quasiperiodic Disorder

We investigate the non-Abelian Thouless pumping in a disorder tunable Lieb chain with degenerate flat bands. The results reveal that quasiperiodic disorder will cause a topological phase transition from the trivial (without non-Abelian Thouless pumping) to the non-trivial (with non-Abelian Thouless pumping) phase. The mechanism behind is that the monopole originally outside the topological region can be driven into the topological region due to the introduction of quasiperiodic disorder. Moreover, since the corresponding monopole will turn into a nodal line to spread beyond the boundaries of the topological region, the system with large disorder strength will result in the disappearance of non-Abelian Thouless pumping. Furthermore, we numerically simulate the Thouless pumping of non-Abelian systems, and the evolution results of center of mass' displacement are consistent with the Chern number. Finally, we discuss the localization properties of the system and find that, similar to [PRL 130, 206401(2023)], the inverse Anderson transition does not occur in the system with the increase of quasiperiodic strength, while the system still maintains the coexistence of localized and extended states.

cond-mat.dis-nn↗

arXiv2023

Exploring Parity Magnetic Effects through Experimental Simulation with Superconducting Qubits

We present the successful realization of four-dimensional (4D) semimetal bands featuring tensor monopoles, achieved using superconducting quantum circuits. Our experiment involves the creation of a highly tunable diamond energy diagram with four coupled transmons, and the parametric modulation of their tunable couplers, effectively mapping momentum space to parameter space. This approach enables us to establish a 4D Dirac-like Hamiltonian with fourfold degenerate points. Moreover, we manipulate the energy of tensor monopoles by introducing an additional pump microwave field, generating effective magnetic and pseudo-electric fields and simulating topological parity magnetic effects emerging from the parity anomaly. Utilizing non-adiabatic response methods, we measure the fractional second Chern number for a Dirac valley with a varying mass term, signifying a nontrivial topological phase transition connected to a 5D Yang monopole. Our work lays the foundation for further investigations into higher-dimensional topological states of matter and enriches our comprehension of topological phenomena.

quant-ph↗

arXiv2023

Quantum quenches in a pseudo-Hermitian Chern insulator

We propose to uncover the topology of a pseudo-Hermitian Chern insulator by quantum quench dynamics. The Bloch Hamiltonian of the pseudo-Hermitian Chern insulator is defined in the basis of the q-deformed Pauli matrices, which are related to the representation of the deformed algebras. We show the bulk-surface duality of the pseudo-Hermitian phases, then further build a concrete relation between the static band topology and quench dynamics, in terms of the time-averaged spin textures. The results are also generalized into a fully nonequilibrium case where the postquench evolution is governed by a Floquet pseudo-Hermitian Hamiltonian. Furthermore, we propose a possible scheme to realize the seemingly challenging model in a bilayer lattice and detect the dynamics with a double-quench protocol.

cond-mat.mes-hall↗

arXiv2023

Second Euler number in four dimensional synthetic matter

Two-dimensional Euler insulators are novel kind of systems that host multi-gap topological phases, quantified by a quantised first Euler number in their bulk. Recently, these phases have been experimentally realised in suitable two-dimensional synthetic matter setups. Here we introduce the second Euler invariant, a familiar invariant in both differential topology (Chern-Gauss-Bonnet theorem) and in four-dimensional Euclidean gravity, whose existence has not been explored in condensed matter systems. Specifically, we firstly define two specific novel models in four dimensions that support a non-zero second Euler number in the bulk together with peculiar gapless boundary states. Secondly, we discuss its robustness in general spacetime-inversion invariant phases and its role in the classification of topological degenerate real bands through real Grassmannians. In particular, we derive from homotopy arguments the minimal Bloch Hamiltonian form from which the tight-binding models of any second Euler phase can be generated. Considering more concretely the gapped Euler phase associated with the tangent bundle of the four-sphere, we show that the bulk band structure of the nontrivial 4D Euler phase necessarily exhibits triplets of linked nodal surfaces (where the three types of nodal surfaces are formed by the crossing of the three successive pairs of bands within one four-band subspace). Finally, we show how to engineer these new topological phases in a four-dimensional ultracold atom setup. Our results naturally generalize the second Chern and spin Chern numbers to the case of four-dimensional phases that are characterised by real Hamiltonians and open doors for implementing such unexplored higher-dimensional phases in artificial engineered systems, ranging from ultracold atoms to photonics and electric circuits.

cond-mat.mes-hall↗

arXiv2022

Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases

Higher-dimensional topological phases play a key role in understanding the lower-dimensional topological phases and the related topological responses through a dimensional reduction procedure. In this work, we present a Dirac-type model of four-dimensional (4D) $\mathbb{Z}_2$ topological insulator (TI) protected by $\mathcal{CP}$-symmetry, whose 3D boundary supports an odd number of Dirac cones. A specific perturbation splits each bulk massive Dirac cone into two valleys separated in energy-momentum space with opposite second Chern numbers, in which the 3D boundary modes become a nodal sphere or a Weyl semimetallic phase. By introducing the electromagnetic (EM) and pseudo-EM fields, exotic topological responses of our 4D system are revealed, which are found to be described by the (4+1)D mixed Chern-Simons theories in the low-energy regime. Notably, several topological phase transitions occur from a $\mathcal{CP}$-broken $\mathbb{Z}_2$ TI to a $\mathbb{Z}$ TI when the bulk gap closes by giving rise to exotic double-nodal-line/nodal-hyper-torus gapless phases. Finally, we propose to probe experimentally these topological effects in cold atoms.

cond-mat.mes-hall↗

arXiv2022

Link between \emph{Zitterbewegung} and topological phase transition

Topological quantum state described by the global invariant has been extensively studied in theory and experiment. In this letter, we investigate the relationship between \emph{Zitterbewegung} and the topology of systems that reflect the properties of the local and whole energy bands, respectively. We generalize the usual two-band effective Hamiltonian to characterize the topological phase transition of the spin-$J$ topological insulator. By studying \emph{Zitterbewegung} dynamics before and after topological phase transition, we find that the direction of quasiparticles' oscillation can well reflect topological properties. Furthermore, we develop a quantitative calculation formula for the topological invariant in the spin-$J$ Chern insulator and give the selection rule of the corresponding dynamics. Finally, we demonstrate that our theory is valid in different topological systems. The topological invariant can be represented by local dynamical properties of the high-symmetry points in the first Brillouin zone, which provides a new measurement method from the dynamical perspective.

quant-ph↗

arXiv2022

Extracting non-Abelian quantum metric tensor and its related Chern numbers

The complete geometry of quantum states in parameter space is characterized by the quantum geometric tensor, which contains the quantum metric and Berry curvature as the real and imaginary parts, respectively. When the quantum states are degenerate, the quantum metric and Berry curvature take non-Abelian forms. The non-Abelian (Abelian) Berry curvature and Abelian quantum metric have been experimentally measured. However, an experimentally feasible scheme to extract all the components of the non-Abelian quantum metric tensor is still lacking. Here we propose a generic protocol to directly extract the non-Abelian quantum metric tensor in arbitrary degenerate quantum states in any dimensional parameter space, based on measuring the transition probabilities after parameter quenches. Furthermore, we show that the non-Abelian quantum metric can be measured to obtain the real Chern number of a generalized Dirac monopole and the second Chern number of a Yang monopole, which can be simulated in three and five-dimensional parameter space of artificial quantum systems, respectively. We also demonstrate the feasibility of our quench scheme for these two applications with numerical simulations.

quant-ph↗

arXiv2021

Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric

Among non-Hermitian systems, pseudo-Hermitian phases represent a special class of physical models characterized by real energy spectra and by the absence of non-Hermitian skin effects. Here, we show that several pseudo-Hermitian phases in two and three dimensions can be built by employing $q$-deformed matrices, which are related to the representation of deformed algebras. Through this algebraic approach we present and study the pseudo-Hermitian version of well known Hermitian topological phases, raging from two-dimensional Chern insulators and time-reversal-invariant topological insulators to three-dimensional Weyl semimetals and chiral topological insulators. We analyze their topological bulk states through non-Hermitian generalizations of Abelian and non-Abelian tensor Berry connections and quantum metric. Although our pseudo-Hermitian models and their Hermitian counterparts share the same topological invariants, their band geometries are different. We indeed show that some of our pseudo-Hermitian phases naturally support nearly-flat topological bands, opening the route to the study of pseudo-Hermitian strongly-interacting systems. Finally, we provide an experimental protocol to realize our models and measure the full non-Hermitian quantum geometric tensor in synthetic matter.

cond-mat.mes-hall↗

arXiv2021

A synthetic monopole source of Kalb-Ramond field in diamond

Magnetic monopoles play a central role in various areas of fundamental physics, ranging from electromagnetism to topological states of matter. While their observation is elusive in high-energy physics, monopole sources of artificial gauge fields have been recently identified in synthetic matter. String theory, a potentially unifying framework that encompasses quantum mechanics, promotes the conventional \emph{vector} gauge fields of electrodynamics to \emph{tensor} gauge fields, and predicts the existence of more exotic \emph{tensor monopoles} in 4D space. Here we report on the characterization of a tensor monopole synthesized in a 4D parameter space by the spin degrees of freedom of a single solid-state defect in diamond. Using two complementary methods, we characterize the tensor monopole by measuring its quantized topological charge and its emanating Kalb-Ramond field. By introducing a fictitious external field that breaks chiral symmetry, we further observe an intriguing transition in the spectrum, characterized by spectral rings protected by mirror symmetries. Our work represents the first detection of tensor monopoles in a solid-state system and opens up the possibility of emulating exotic topological structures inspired by string theory.

quant-ph↗

arXiv2020

Tensor monopoles and negative magnetoresistance effect in optical lattices

We propose that a kind of four-dimensional (4D) Hamiltonians, which host tensor monopoles related to quantum metric tensor in even dimensions, can be simulated by ultracold atoms in the optical lattices. The topological properties and bulk-boundary correspondence of tensor monopoles are investigated in detail. By fixing the momentum along one of the dimensions, it can be reduced to an effective three-dimensional model manifesting with a nontrivial chiral insulator phase. Using the semiclassical Boltzmann equation, we calculate the longitudinal resistance against the magnetic field $B$ and find the negative relative magnetoresistance effect of approximately $ -B^{2} $ dependence when a hyperplane cuts through the tensor monopoles in the parameter space. We also propose an experimental scheme to realize this 4D Hamiltonian by introducing an external cyclical parameter in a 3D optical lattice. Moreover, we show that the quantum metric tensor and Berry curvature can be detected by applying an external drive in the optical lattices.

cond-mat.mes-hall↗

arXiv2020

Four-dimensional semimetals with tensor monopoles: From surface states to topological responses

Quantum anomalies offer a useful guide for the exploration of transport phenomena in topological semimetals. In this work, we introduce a model describing a semimetal in four spatial dimensions, whose nodal points act like tensor monopoles in momentum space. This system is shown to exhibit monopole-to-monopole phase transitions, as signaled by a change in the value of the topological Dixmier-Douady invariant as well as by the associated surface states on its boundary. We use this model to reveal an intriguing "4D parity magnetic effect", which stems from a parity-type anomaly. In this effect, topological currents are induced upon time-modulating the separation between the fictitious monopoles in the presence of a magnetic perturbation. Besides its theoretical implications in both condensed matter and quantum field theory, the peculiar 4D magnetic effect revealed by our model could be measured by simulating higher-dimensional semimetals in synthetic matter.

cond-mat.mes-hall↗

arXiv2019

Note on "Experimental Measurement of Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit"

In the paper [X. Tan et al., Phys. Rev. Lett. 122, 210401 (2019)], we have studied the Euler characteristic number $χ$ for a two-band model; However, the calculated $χ$ there is not an integer when the parameter $|h|>1$ and then may not be considered as a suitable topological number for the system. In this note, we find that the Bloch vectors of the ground state for $|h|>1$ do not cover the whole Bloch sphere and thus the Euler characteristic number should be effectively associated with the manifold of a disk, rather than a sphere. After taking into account the boundary contribution, we derive the correct Euler characteristic number. Unfortunately, the Euler characteristic number does not change when crossing the critical points $|h|=1$ and thus can not be used to characterize the topological phase transition of the present model.

quant-ph↗