arXiv subjects

Jiong-Hao Wang

Publications and source records attributed to Jiong-Hao Wang.

16 recordsLinked to original sources

arXiv2026

Fractional Chern Insulators in Twisted Bilayer Optical Lattices

Twisted bilayer materials provide a versatile platform for realizing correlated topological states. Motivated by the recent experimental realization of atomic Bose-Einstein condensates in twisted bilayer optical lattices, we investigate the emergence of fractional topological phases in such systems. For experimentally realistic parameters, the single-particle spectrum hosts a pair of quasi-degenerate nearly flat moiré bands. We show using self-consistent Hartree-Fock calculations that atomic interactions spontaneously break time-reversal symmetry, lift the quasi-degeneracy, and generate an isolated nearly flat band with a nonzero Chern number. At fractional filling, exact diagonalization of the Hamiltonian projected to this band reveals a threefold degenerate ground-state manifold and a characteristic particle entanglement spectrum, providing strong evidence for a fractional Chern insulator. The resulting many-body gap is of order $10^{-3}E_R$, corresponding to a nanokelvin energy scale accessible to state-of-the-art cold-atom experiments. Our scheme requires neither spin-orbit coupling, as in transition metal dichalcogenides, nor a finite magnetic field, as in existing twisted-bilayer-graphene experiments, providing a highly tunable route to strongly correlated topological phases in twisted bilayer optical lattices.

cond-mat.quant-gas↗

arXiv2026

Quantum spin Hall crystals at fractional filling of twisted MoTe$_2$

We predict and classify interaction-driven quantum spin Hall crystals (QSHCs), a class of states emerging at fractional filling through an interplay of topology and spontaneous translation-symmetry breaking. QSHCs form nearly degenerate manifolds whose members can realize distinct topological phases protected by time-reversal or valley $U(1)_v$ symmetry, with time-reversal acting nontrivially within the manifold. As a representative of this broad class of states we provide evidence for 9-fold quasi-degenerate $\sqrt{3}\times\sqrt{3}$ charge ordered QSHCs at $ν= -8/3$ of twisted bilayer MoTe$_2$ near a $5^\circ$ twist. Here a $\mathbb{Z}_3$ index organizes states related by lattice translation into three time-reversal invariant states with nontrivial $\mathbb{Z}_2$ topology and three time-reversal related doublets whose individual members spontaneously break time-reversal and carry a $U(1)_v$ protected spin-Chern number. Finally, we determine the conditions that favor QSHCs over closely competing intervalley-coherent crystals.

cond-mat.str-el↗

arXiv2026

Anomalous quantized nonlinear soliton pumping

It has recently been theoretically predicted and experimentally observed that a soliton resulting from nonlinearity can be pumped across an integer or fractional number of unit cells as a system parameter is slowly varied over a pump period. Nonlinear soliton pumping is now understood as the flow of instantaneous Wannier functions, ruling out the possibility of pumping a soliton across a nonzero number of unit cells over one cycle when a corresponding Wannier function does not exhibit any flow, i.e., when the corresponding Bloch band that the soliton bifurcates from is topologically trivial. Here we surprisingly find an anomalous nonlinear soliton pump where the displacement of a soliton over one cycle differs from the Chern number of the Bloch band from which the soliton comes. We show that this anomalous behavior arises from a transition of a soliton between different Wannier functions by passing through an intersite-soliton (or dipole-soliton) state. Furthermore, we find a nonlinearity-induced integer quantized pump of a soliton, allowing a soliton to travel across one unit cell during a pump period, even when the corresponding band is topologically trivial. Our results open the door to studying nonlinearity-induced pumping of solitons.

nlin.PS↗

arXiv2026

Topological Order and Non-Hermitian Skin Effect in Generalized Ideal Chern Bands

Fractionalization in ideal Chern bands and non-Hermitian topological physics are two active but so far separate research directions. Merging these, we generalize the notion of ideal Chern bands to the non-Hermitian realm and uncover several striking consequences both on the level of band theory and in the strongly interacting regime. Specifically, we show that the lowest band of a Kapit--Mueller lattice model with an imaginary gauge potential satisfies a generalized ideal condition with complex Berry curvature in sync with a complex quantum metric. The ideal band remains purely real and exactly flat on both the torus and cylinder: eigenstates are extended on the torus, while on the cylinder all right and left eigenstates localize at the boundaries, yielding a non-Hermitian skin effect without spectral winding. In the interacting regime, we find that the generalized ideal condition stabilizes an incompressible liquid at fractional fillings, retaining intrinsic non-Hermitian features on both cylinder and torus, while strikingly distinct on different manifolds. On the cylinder, the ground states are always skin-Laughlin states. In contrast, on the torus, we instead observe an unconventional competition between topologically ordered Laughlin-like states and negative collective modes, arising purely from non-Hermiticity.

cond-mat.mes-hall↗

arXiv2026

Filling-Sensitive Spectral Complexity from Hilbert-Space Holonomy in Fragmented Non-Hermitian Systems

We show that Hilbert-space holonomy provides a geometric organizing principle for spectral reality in fragmented non-Hermitian many-body systems, complementary to conventional symmetry protection. In two minimal fragmented models, complex spectra can arise only within the most symmetric sectors: half filling in the fermion model and zero magnetization in the spin chain. Adding or removing a single particle, or flipping a single spin, renders the spectra entirely real despite unchanged periodic boundary conditions, reminiscent of boundary-condition sensitivity in systems with a non-Hermitian skin effect. We explain this by viewing nonreciprocal hopping amplitudes as a discrete gauge field on the Krylov graph: trivial holonomy permits a diagonal similarity transformation to the Hermitian limit, whereas nontrivial holonomy obstructs it and allows complex spectra. In certain regimes, trivial holonomy admits an emergent-boundary interpretation, and longer-range models exhibit finite real and complex regions governed by the same criterion.

cond-mat.str-el↗

arXiv2025

Observation of topological phases without crystalline counterparts

Topological phases have been extensively studied primarily in crystalline systems with translational symmetry. Recent theoretical studies, however, have demonstrated the existence of topological phases in quasicrystals that are absent in crystals. Despite numerous experimental observations of topological phases in various crystalline systems, observing these phases without crystalline counterparts remains challenging due to very complex models. Here, we design a practically realizable tight-binding model with nearest-neighbor hopping on the Ammann-Beenker quasicrystalline lattice. This model respects eight-fold rotational and chiral symmetries, resulting in a higher-order topological phase with eight zero-energy corner modes that have no crystalline counterparts. We experimentally explore the topological phase in an acoustic quasicrystal. Surprisingly, we also discover symmetry-protected zero-energy modes near the center of the quasicrystal in a topologically trivial phase, a phenomenon not seen in crystals. We further experimentally observe these modes in a topologically trivial acoustic quasicrystal. Our work represents the first experimental observation of topological phases in quasicrystals without crystalline counterparts, paving the way for the study of exotic topological physics in quasicrystals.

cond-mat.mes-hall↗

arXiv2025

Transitions from Composite Fermi Liquid to Moore-Read States in Weyl Semimetals

Weyl semimetals represent a significant class of topological gapless materials in three dimensions and have been shown to exhibit three-dimensional quantum Hall effect. However, existing research mainly focuses on scenarios without interactions. Recent studies suggest that the fractional quantum Hall effect can arise in a Weyl semimetal with a one-third filled Landau level under a magnetic field. However, it remains unclear whether more exotic states, such as composite Fermi liquid and MooreRead states, can appear at half filling. Here we surprisingly find the existence of composite Fermi liquid, Moore-Read states and charge density waves in the same Weyl-orbit-based Landau level of a Weyl semimetal and their transitions induced by varying the distance between Weyl points. We attribute these transitions to a significant change in the single-particle wave functions of the Landau level as the distance between Weyl points is varied. Finally, we demonstrate that a transition from composite Fermi liquid to Moore-Read states can be induced by tuning the direction of a magnetic field, a process that is more experimentally accessible.

cond-mat.mes-hall↗

arXiv2025

Three-Dimensional Quantum Hall Effect in Topological Amorphous Metals

Weyl semimetals have been theoretically predicted to become topological metals with anomalous Hall conductivity in amorphous systems. However, measuring the anomalous Hall conductivity in realistic materials, particularly those with multiple pairs of Weyl points, is a significant challenge. If a system respects time-reversal symmetry, then the anomalous Hall conductivity even vanishes. As such, it remains an open question how to probe the Weyl band like topology in amorphous materials. Here, we theoretically demonstrate that, under magnetic fields, a topological metal slab in amorphous systems exhibits three-dimensional quantum Hall effect, even in time-reversal invariant systems, thereby providing a feasible approach to exploring Weyl band like topology in amorphous materials. We unveil the topological origin of the quantized Hall conductance by calculating the Bott index. The index is carried by broadened Landau levels with bulk states spatially localized except at critical transition energies.The topological property also results in edge states localized at distinct hinges on two opposite surfaces.

cond-mat.mes-hall↗

arXiv2025

Fractional Quantum Hall Effect Based on Weyl Orbits

The fractional quantum Hall effect is a well-known demonstration of strongly correlated topological phases in two dimensions. However, the extension of this phenomenon into a three-dimensional context has yet to be achieved. Recently, the three-dimensional integer quantum Hall effect based on Weyl orbits has been experimentally observed in a topological semimetallic material under a magnetic field. This motivates us to ask whether the Weyl orbits can give rise to the fractional quantum Hall effect when their Landau level is partially filled in the presence of interactions. Here we theoretically demonstrate that the fractional quantum Hall states based on Weyl orbits can emerge in a Weyl semimetal when a Landau level is one-third filled. Using concrete models for Weyl semimetals in magnetic fields, we project the Coulomb interaction onto a single Landau level from the Weyl orbit and find that the ground state of the many-body Hamiltoian is triply degenerate. We further show that the ground states exhibit the many-body Chern number of $1/3$ and the uniform occupation of electrons in both momentum and real space, implying that they are the fractional quantum Hall states. In contrast to the two-dimensional case, the states are spatially localized on two surfaces hosting Fermi arcs. Additionally, our findings suggest that the excitation properties of these states resemble those of the Laughlin state in two dimensions, as inferred from the particle entanglement spectrum of the ground states.

cond-mat.str-el↗

arXiv2024

Higher-order topological phases in crystalline and non-crystalline systems: a review

In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases due to the higher-order bulk-boundary correspondence. In this review, we summarize current research progress on higher-order topological phases in both crystalline and non-crystalline systems. We firstly introduce prototypical models of higher-order topological phases in crystals and their topological characterizations. We then discuss effects of quenched disorder on higher-order topology and demonstrate disorder-induced higher-order topological insulators. We also review the theoretical studies on higher-order topological insulators in amorphous systems without any crystalline symmetry and higher-order topological phases in nonperiodic lattices including quasicrystals, hyperbolic lattices, and fractals, which have no crystalline counterparts. We conclude the review by a summary of experimental realizations of higher-order topological phases and discussions on potential directions for future study.

cond-mat.mes-hall↗

arXiv2023

Average Symmetry Protected Higher-order Topological Amorphous Insulators

While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline counterparts. Here we theoretically demonstrate the existence of higher-order topological insulators in two-dimensional amorphous systems that can host more than six corner modes, such as eight or twelve corner modes. Although individual sample configuration lacks crystalline symmetry, we find that an ensemble of all configurations exhibits an average crystalline symmetry that provides protection for the new topological phases. To characterize the topological phases, we construct two topological invariants. Even though the bulk energy gap in the topological phase vanishes in the thermodynamic limit, we show that the bulk states near zero energy are localized, as supported by the level-spacing statistics and inverse participation ratio. Our findings open an avenue for exploring average symmetry protected higher-order topological phases in amorphous systems without crystalline counterparts.

cond-mat.dis-nn↗

arXiv2023

Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts

Quasicrystals allow for symmetries that are impossible in crystalline materials, such as eight-fold rotational symmetry, enabling the existence of novel higher-order topological insulators in two dimensions without crystalline counterparts. However, it remains an open question whether three-dimensional higher-order topological insulators and Weyl-like semimetals without crystalline counterparts can exist. Here, we demonstrate the existence of a second-order topological insulator by constructing and exploring a three-dimensional model Hamiltonian in a stack of Ammann-Beenker tiling quasicrystalline lattices. The topological phase has eight chiral hinge modes that lead to quantized longitudinal conductances of $4 e^2/h$. We show that the topological phase is characterized by the winding number of the quadrupole moment. We further establish the existence of a second-order topological insulator with time-reversal symmetry, characterized by a $\mathbb{Z}_2$ topological invariant. Finally, we propose a model that exhibits a higher-order Weyl-like semimetal phase, demonstrating both hinge and surface Fermi arcs. Our findings highlight that quasicrystals in three dimensions can give rise to higher-order topological insulators and semimetal phases that are unattainable in crystals.

cond-mat.mes-hall↗

arXiv2023

Quadrupole Insulator without Corner States in the Energy Spectrum

The quadrupole insulator is a well-known instance of higher-order topological insulators in two dimensions, which possesses midgap corner states in both the energy spectrum and entanglement spectrum. Here, by constructing and exploring a model Hamiltonian under a staggered $\mathbb{Z}_2$ gauge field that respects momentum-glide reflection symmetries, we surprisingly find a quadrupole insulator that lacks zero-energy corner modes in its energy spectrum, despite possessing a nonzero quadrupole moment. Remarkably, the existence of midgap corner modes is found in the entanglement spectrum. Since these midgap states cannot be continuously eliminated, the quadrupole insulator cannot be continuously transformed into a trivial topological insulator, thereby confirming its topological nature. We show that the breakdown of the correspondence between the energy spectrum and entanglement spectrum occurs due to the closure of the edge energy gap when the Hamiltonian is flattened. Finally, we present a model that demonstrates an insulator with corner modes in the energy spectrum even in the absence of the quadrupole moment. In this phase, the entanglement spectrum does not display any midgap states. The results suggest that the bulk-edge correspondence of quadrupole insulators generally manifests in the entanglement spectrum rather than the energy spectrum.

cond-mat.mes-hall↗

arXiv2021

Symmetry-Protected Topological Phases in a Rydberg Glass

Recent theoretical studies predict that structural disorder, serving as a bridge connecting a crystalline material to an amorphous material, can induce a topological insulator from a trivial phase. However, to experimentally observe such a topological phase transition is very challenging due to the difficulty in controlling structural disorder in a quantum material. Given experimental realization of randomly positioned Rydberg atoms, such a system is naturally suited to studying structural disorder induced topological phase transitions and topological amorphous phases. Motivated by the development, we study topological phases in an experimentally accessible one-dimensional amorphous Rydberg atom chain with random atom configurations. In the single-particle level, we find symmetry-protected topological amorphous insulators and a structural disorder induced topological phase transition, indicating that Rydberg atoms provide an ideal platform to experimentally observe the phenomenon using state-of-the-art technologies. Furthermore, we predict the existence of a gapless symmetry-protected topological phase of interacting bosons in the experimentally accessible system. The resultant many-body topological amorphous phase is characterized by a $\mathbb{Z}_2$ invariant.

cond-mat.dis-nn↗

arXiv2021

Anomalous Transport Induced by Non-Hermitian Anomalous Berry Connection in Non-Hermitian Systems

Non-Hermitian materials can not only exhibit exotic energy band structures but also an anomalous velocity induced by non-Hermitian anomalous Berry connection as predicted by the semiclassical equations of motion for Bloch electrons. However, it is not clear how the modified semiclassical dynamics modifies transport phenomena. Here, we theoretically demonstrate the emergence of anomalous oscillations driven by either an external dc or ac electric field, which arise from non-Hermitian anomalous Berry connection. Moreover, it is a well-known fact that geometric structures of electric wave functions can only affect the Hall conductivity. However, we are surprised to find a non-Hermitian anomalous Berry connection induced anomalous linear longitudinal conductivity independent of the scattering time. We also show the emergence of a second-order nonlinear longitudinal conductivity induced by non-Hermitian anomalous Berry connection, violating a well-known fact of its absence in a Hermitian system with symmetric energy spectra. These anomalous phenomena are illustrated in a pseudo-Hermitian system with large non-Hermitian anomalous Berry connection. Finally, we propose a practical scheme to realize the anomalous oscillations in an optical system.

cond-mat.mes-hall↗

arXiv2021

Structural Disorder Induced Second-order Topological Insulators in Three Dimensions

Higher-order topological insulators are established as topological crystalline insulators protected by crystalline symmetries. One celebrated example is the second-order topological insulator in three dimensions that hosts chiral hinge modes protected by crystalline symmetries. Since amorphous solids are ubiquitous, it is important to ask whether such a second-order topological insulator can exist in an amorphous system without any spatial order. Here we predict the existence of a secondorder topological insulating phase in an amorphous system without any crystalline symmetry. Such a topological phase manifests in the winding number of the quadrupole moment, the quantized longitudinal conductance and the hinge states. Furthermore, in stark contrast to the viewpoint that structural disorder should be detrimental to the higher-order topological phase, we remarkably find that structural disorder can induce a second-order topological insulator from a topologically trivial phase in a regular geometry. We finally demonstrate the existence of a second-order topological phase in amorphous systems with time-reversal symmetry.

cond-mat.mes-hall↗