arXiv subjects

Taige Wang

Publications and source records attributed to Taige Wang.

At least 19 recordsLinked to original sources

arXiv2026

Entangling power of neural networks

Characterizing the complexity of correlations between subsystems is a fundamental task across information theory, machine learning, and science. In quantum physics, neural networks have found increasing application in learning wavefunctions. Here we introduce the entangling power of an encoder-decoder neural network, which quantifies its ability to generate entanglement between subsystems, dependent on a latent space dimension $K$ and the complexity class of the decoder. We exactly calculate this quantity for polynomial decoders of degree $p$ acting on a $K$-dimensional latent space. Our results establish the exponential entangling power of neural networks with modest resources. More broadly, our work provides a framework for analyzing correlations in machine learning that generalizes the notion of the Schmidt rank in entanglement theory.

cond-mat.dis-nn↗

arXiv2026

Periodic solution and its stability of a damped BBM equation posed on $\mathbb{T}$

In this paper, we are concerned with the existence and stability of temporal periodic solutions to a class of the Benjamin-Bona-Mahony (BBM) equation with damping in the torus $\mathbb{T}$, whose interior is applied with periodic force $f(x, t)$ with temporal period $\theta$. These types of solutions are established in $H^{\ell}, \ell\ge 0$, and it is noteworthy to see that the I-energy method is invoked when low regularity of $\ell\in[0, 1)$ is pursued.

math.AP↗

arXiv2026

Quantum Mott semimetal in a one-dimensional Hubbard model

Mott physics in topological bands has recently attracted considerable attention, particularly in the context of twisted bilayer graphene (TBG). However, the essential ingredients for stabilizing this physics remain unclear. Here, we demonstrate a quantum Mott semimetal phase as the ground state within a one-dimensional spinful Hubbard model featuring only one orbital per unit cell, protected by inversion and particle-hole symmetries. We start from a two-orbital model where a localized $f$ orbital on the A sublattice hybridizes with a delocalized $c$ orbital on the B sublattice. Projecting the $f$-orbital Hubbard $U$ onto the active flat band yields a lattice model with Wannier orbitals centered on the B sublattice. Similar to TBG, a momentum-space scale $k_*$ emerges, setting the interaction range in the projected model to $1/k_*$. While the ground state is ferromagnetic with only the Hubbard $U$, introducing an inter-site antiferromagnetic spin coupling $J$ stabilizes a Mott semimetal$^*$ phase with a central charge $c=3$. Using exact diagonalization (ED) and density matrix renormalization group (DMRG) methods, we show that this phase hosts a spinful Dirac fermion coexisting with a neutral spin mode -- analogous to the fractionalized Fermi liquid (FL$^*$) phase in higher dimensions. Furthermore, breaking particle-hole (PH) symmetry via dispersion transforms the Mott semimetal into a Mott insulator, which is separated from a distinct Mott insulating phase by a continuous transition with a polarization jump of $1/2$. Our work provides the first unbiased evidence of a Mott semimetal ground state and demonstrates that this 1D model captures some essential aspects of TBG physics, despite lacking a Wannier obstruction.

cond-mat.str-el↗

arXiv2026

Simulating quantum circuits with a neural statebank

Predicting the output of quantum circuits is a central bottleneck for verifying quantum processors because a generic wavefunction grows exponentially with system size. We introduce a neural statebank that learns this wavefunction along the circuit trajectory. Each layer is stored as an autoregressive Transformer checkpoint trained from local gate updates to the preceding checkpoint, producing a compact neural representation that can evaluate amplitudes and generate independent samples. On long-range circuits combining entanglement, magic, and non-diagonal branching, a 0.3-million-parameter statebank reaches $\sim 10^{-2}$ infidelity at 34 qubits, outperforming the other tested approximate simulators while using far less memory than exact state-vector evolution. The same architecture accurately simulates quantum approximate optimization, Clifford+$T$, and Clifford circuits.

quant-ph↗

arXiv2026

Measuring anyon dispersion with tunneling probes

Anyons are usually characterized by their topological data and their fractional quantum numbers under global symmetries. In lattice systems such as fractional Chern insulators (FCI), they are also mobile quasiparticles. Their motion controls the possible ground states of the dilute anyon gas obtained by doping an FCI, including possible superconducting states. We show how tunneling probes can measure this motion. In scanning tunneling spectroscopy, weak disorder produces spatially oscillating quasiparticle-interference patterns whose branches reveal the dispersion of fractionalized constituents. In quantum twisting microscopy, planar momentum-conserving tunneling selects the total momentum of the injected electron, so the continuum thresholds of fractionalized electron spectra encode the dispersion of the constituent anyons. The resulting spectra distinguish compact electron-like excitations, bound anyon molecules, and unbound anyon continuum.

cond-mat.mes-hall↗

arXiv2026

Topological superconductivity from Abelian fractional Chern insulators

Can a Laughlin anyon fluid become a topological superconductor? We answer this question for a $\nu=1/3$ fractional Chern insulator (FCI) using a $U(3)$ infrared parton theory. Three charge-$e/3$ constituents form the electron, while three constituent pairs form a gauge-invariant charge-$2e$ Cooper pair. The resulting superconductors share an ordinary charge-$2e$ sector but differ in their neutral color response, giving an SC$^\ast$ with the parent Laughlin $U(1)_3$ order, a chiral topological superconductor with $c_-=3/2$, and a strong-pairing molecular superconductor with $c_-=3$. The same framework organizes a nearby $\sigma_{xy}=0$ charge density wave (CDW) state. At commensurate filling, the normal state and the $c_-=3$ and $c_-=3/2$ superconducting descendants are naturally tied to a period-three density order background, while the SC$^\ast$ branch can preserve microscopic translations. Away from commensuration, a chargon metal can pair into the same $c_-=3/2$ topological superconductor. The FCI, reentrant CDW, and chiral superconductivity are unified in the $U(3)$ parton theory.

cond-mat.str-el↗

arXiv2026

Van Hove Singularity-Driven Topological Magnetism in Twisted MoTe2

Van Hove singularities (vHSs) strongly amplify electron interactions and can stabilize correlated phases in topological bands. Here we report signatures of topological magnetism in large-angle twisted bilayer MoTe2 driven by the interplay of vHSs, strong correlations, and valley topology. In a 4.8 degree device, electrostatic tuning to a vHS produces a spontaneous anomalous Hall hot spot near nu = -1. Combined transport and reflective magnetic circular dichroism measurements indicate that this regime is not governed by magnetization alone, but instead emerges from a correlated intervalley-coherent antiferromagnetic state that evolves with doping into a canted phase. With increasing magnetic field, the Hall response develops an additional finite-field component consistent with a topological Hall effect from a noncoplanar spin texture, before transitioning into a C = -1 Chern insulator. Our results establish tunable vHSs in moire topological bands as a route to chiral magnetism and engineering topological phase transitions.

cond-mat.mes-hall↗

arXiv2026

Studying 3D O(N) Surface CFT on the Fuzzy Sphere

Boundary conformal field theory (BCFT) provides a universal framework for critical phenomena in the presence of boundaries. We determine BCFT data for the normal and ordinary boundary universality classes of the $1+1$-dimensional boundaries of the $2+1$-dimensional $O(2)$ and $O(3)$ Wilson-Fisher fixed points, realized microscopically by a bilayer Heisenberg model on the fuzzy sphere. Using the fuzzy-sphere state-operator correspondence, we obtain boundary operator spectra, identify low-lying boundary primary operators, extract operator-product-expansion (OPE) data, and estimate the boundary central charges for both boundary conditions. For the normal boundary condition, the universal amplitudes $a_\sigma$ and $b_t$ extracted from one- and two-point functions agree quantitatively with Monte Carlo benchmarks where available. For both $N=2$ and $N=3$, we find a positive extraordinary-log exponent $\alpha$, providing independent microscopic evidence for extraordinary-log boundary criticality. Our results extend fuzzy-sphere BCFT spectroscopy beyond the Ising universality class to continuous $O(N)$ symmetry.

cond-mat.str-el↗

arXiv2026

Anyon molecules in fractional quantum Hall states

We use segment DMRG on the infinite cylinder to compute energies of charged excitations in gate-screened fractional quantum Hall states. For the $\nu=1/3$ Laughlin, $\nu=2/5$ Jain, and $\nu=5/2$ anti-Pfaffian states, we find screening can bind like-charged anyons into molecules, with a strong dependence on filling-factor, gate distance, and fusion channel. In the Laughlin state, stable $\pm 2e/3$ molecules and larger clusters appear over a broad gate-distance window. The Jain state is molecular throughout the range we consider. In the anti-Pfaffian, binding is strongest on the hole side, where the charge-$e/2$ molecule is fused into the $\psi$ channel over a broad window of gate distances. In all three cases, screening suppresses long-range repulsion and exposes an intermediate-range attraction encoded in the oscillatory density tail of the fundamental anyon. We discuss consequences for addition spectra, interferometry, Wigner crystallization, anyon superconductivity, and entropy measurements.

cond-mat.mes-hall↗

arXiv2026

Expressibility of neural quantum states: a Walsh-complexity perspective

Neural quantum states are powerful variational wavefunctions, but it remains unclear which many-body states can be represented efficiently by modern additive architectures. We introduce Walsh complexity, a basis-dependent measure of how broadly a wavefunction is spread over parity patterns. States with an almost uniform Walsh spectrum require exponentially large Walsh complexity from any good approximant. We show that shallow additive feed-forward networks cannot generate such complexity in the tame regime, e.g. polynomial activations with subexponential parameter scaling. As a concrete example, we construct a simple dimerized state prepared by a single layer of disjoint controlled-$Z$ gates. Although it has only short-range entanglement and a simple tensor-network description, its Walsh complexity is maximal. Full-cube fits across system size and depth are consistent with the complexity bound: for polynomial activations, successful fitting appears only once depth reaches a logarithmic scale in $N$, whereas activation saturation in $\tanh$ produces a sharp threshold-like jump already at depth $3$. Walsh complexity therefore provides an expressibility axis complementary to entanglement and clarifies when depth becomes an essential resource for additive neural quantum states.

cond-mat.str-el↗

arXiv2026

Bound states of anyons: a geometric quantization approach

The question of anyon interactions and their possible binding plays a key role in the physics of fractional quantum Hall states. Here, we introduce a controlled and scalable approach to study anyon binding by working entirely within the Hilbert space of anyons. The resulting theory is characterized by an effective potential, which captures the electrostatic energy of classical anyon configurations, and a K\"ahler potential, which simultaneously encodes the anyon Berry phase and the structure of their Hilbert space; both quantities are readily computed using Monte Carlo methods for large systems, enabling reliable extrapolation to the thermodynamic limit. By applying the formalism of geometric quantization on K\"ahler manifolds, we construct the anyon Hamiltonian, which can be exactly diagonalized in the few-anyon Hilbert space. Applying our approach to the quasiholes of the $\nu=1/3$ Laughlin state with screened Coulomb interaction, we find that Laughlin quasiholes form bound states for screening lengths comparable or smaller than the magnetic length. Remarkably, binding occurs despite both the bare electron-electron interaction and the quasihole electrostatic potential being purely repulsive. The bound-state formation is a Berry phase effect, driven by oscillations in the quasihole density profile on the $\ell_B$ scale that are invisible in the quasihole electrostatic potential alone. For multiple quasiholes, we identify a sequence of phases as the screening length is reduced: free $e/3$ anyons, paired $2e/3$ bound states, three-anyon charge-$e$ clusters, and larger composite objects. Finally, we discuss possible signatures in charge imaging experiments on quantum Hall systems and the relevance to the phase diagram of itinerant anyon phases in fractional quantum anomalous Hall materials.

cond-mat.str-el↗

arXiv2026

Forced oscillation of a damped BBM equation posed on whole line in low regularity spaces

In this manuscript, we would established in low regularity spaces $H^\ell, \ell\in [0,1)$, the existence and stability results of time-periodic solution of 1D Cauchy problem of forced damped Benjamin-Bona-Mahony equation (BBM). We use estimates from I-energy method to derive needed estimates in $H^\ell$ for the linearized problem, then convection term will be treated as perturbation of linear problem such that original Cauchy problem is solved.

math.AP↗

arXiv2025

Ferrofluids under oscillatory magnetic fields

Ferrofluids exhibit two canonical interfacial instabilities, a static Rosensweig (normal-field) instability that produces a lattice of peaks and a dynamical Faraday instability that produces parametrically excited standing waves. Here we present a systematic phase diagram of ferrofluid surface states driven by a purely AC vertical magnetic field with zero mean. Scanning a broad range of frequencies and field amplitudes, we resolve two robust branches: a Faraday-wave regime that includes a stable square lattice and a Rosensweig-like peak--valley regime indistinguishable in morphology from Rosensweig peaks. The Faraday-onset boundary is well described by a power law close to $\sqrt{f}$, while the Rosensweig-like peak onset becomes essentially frequency independent at low viscosity. The wave vector of the square lattice grows linearly with frequency over our accessible band. We present a surface-wave theory that captures the full phenomenology, including the emergence of Rosensweig peaks under zero-mean AC driving, the near-$\sqrt{f}$ scaling of the phase boundaries, the linear growth of the selected wave vector with frequency, and the preference for square over hexagonal lattices.

cond-mat.soft↗

arXiv2025

Visualizing interaction-driven restructuring of quantum Hall edge states

Many topological phases host gapless boundary modes that can be dramatically modified by electronic interactions. Even for the long-studied edge modes of quantum Hall phases, forming at the boundaries of two-dimensional (2D) electron systems, the nature of such interaction-induced changes has been elusive. Despite advances made using local probes, key experimental challenges persist: the lack of direct information about the internal structure of edge states on microscopic scales, and complications from edge disorder. Here, we use scanning tunneling microscopy (STM) to image pristine electrostatically defined quantum Hall edge states in graphene with high spatial resolution and demonstrate how correlations dictate the structures of edge channels on both magnetic and atomic length scales. For integer quantum Hall states in the zeroth Landau level, we show that interactions renormalize the edge velocity, dictate the spatial profile for copropagating modes, and induce unexpected edge valley polarization that differ from those of the bulk. While some of our findings can be understood by mean-field theory, others show breakdown of this picture, highlighting the roles of edge fluctuations and inter-channel couplings. We also extend our measurements to spatially resolve the edge state of fractional quantum Hall phases and detect spectroscopic signatures of interactions in this chiral Luttinger liquid. Our study establishes STM as a promising tool for exploring edge physics of the rapidly expanding 2D topological phases, including newly realized fractional Chern insulators.

cond-mat.mes-hall↗

arXiv2025

On periodic solutions of the Benjamin-Bona-Mahony-Burgers equation

In this paper, we would establish the existence and stability of periodic solutions to the Benjamin-Bona-Mahony-Burgers (BBM-Burgers) equation in $H^1_0([0, 1])$, whose medium interior is applied with time-periodic force $f(x, t)$ with period $\theta$. High regularity analysis has been conducted in Hilbert spaces $H^\ell, \ell>1$. We also consider periodic solution to same IBVP scenario of a pseudo-parabolic-regularized equation as an extension of the BBM-Burgers in $\mathcal{H}^{\ell}, \ell=\{1, 2\}$.

math.AP↗

arXiv2025

Anyon superfluidity of excitons in quantum Hall bilayers

The charged anyons of a fractional quantum Hall fluid are necessarily dispersionless due to the continuous magnetic translation symmetry. Neutral anyons, however, can disperse, resulting in a much richer space of possible ``daughter'' states when doped to finite density. We discuss a natural realization of such physics in quantum Hall bilayers, where a finite density of excitons with fractional statistics is argued to give rise to `anyonic exciton superfluidity,' the charge-neutral analog of anyon superconductivity. In a balanced bilayer of two Laughlin $\nu = 1/3$ states, the minimal interlayer exciton carries anyonic exchange statistics. A finite density of these excitons is argued to yield an exciton superfluid stitched to a specific bulk topological order and edge spectrum. Such superfluidity should be most robust near the direct transition into the Halperin $(112)$ state, and near analogous transitions in the bilayer Jain sequence at total filling $\nu_\text{T} = 2\times \frac{n}{2n+1}$. These topological transitions can be described by Chern-Simons QED$_3$, from which we derive several novel and general properties of anyon superfluidity near such transitions, including an anomalously large superfluid stiffness of $\kappa_\text{s} \propto |\delta\nu|^{1/2}$ at layer imbalance fraction $\delta\nu$. A notable feature of the phase diagrams we construct is the prevalence of spatial symmetry breaking, driven by an underlying composite Fermi surface. Our results can be directly tested with currently available experimental techniques. We compare our theory with existing data and make concrete predictions for future measurements, including higher-pseudospin exciton superfluids when doping higher Jain fractions.

cond-mat.str-el↗

arXiv2025

Anyon superfluid in trilayer quantum Hall systems

Intertwining intrinsic topological order with gapless collective modes remains a central challenge in many-body physics. We show that a quantum-Hall trilayer at $\nu_{1}=\nu_{2}=\nu_{3}= \frac13$, tuned solely by the inter-layer spacing $d$, realizes this goal. Large-scale density-matrix renormalization group (DMRG) calculations and a Chern-Simons field theory analysis reveal an intermediate ``anyon-exciton condensate'' separating the familiar $\nu_{\mathrm{tot}}=1$ exciton condensate ($d \to 0$) from three decoupled Laughlin liquids ($d \to \infty$). In this phase, neutral bi-excitons condense while a $\nu=\frac23$ Laughlin topological order survives, yielding a Goldstone mode coexisting with fractionalized anyons. A Ginzburg-Landau analysis maps out the finite-temperature phase diagram. The anyon-exciton condensate can be experimentally verified through a vanishing double-counter-flow resistance and a fractional layer-resolved Hall resistivity $R_{xy}=\frac{5}{2} h/e^{2}$, both within reach of existing high-mobility trilayer devices.

cond-mat.str-el↗

arXiv2025

Propagating Collective Spin-valley Modes in Twisted WSe2

The emergence of neutral collective modes is a hallmark of correlated quantum phases but is often challenging to probe experimentally. In two-dimensional flatband systems, charge responses have been intensively investigated yet neutral excitations remain largely unexplored. In particular, intervalley coherent state (IVC) features a neutral Goldstone mode due to spontaneously broken valley U(1) symmetry. While IVC state has been proposed as a unifying theme across graphene and semiconductor based systems, its defining feature, the neutral Goldstone mode, remains elusive in experiment. Here we investigate space and time resolved transport of neutral modes in twisted WSe2 moire superlattices through a novel ultrafast imaging technique. We uncover two new propagating collective modes with very different velocities, which emerge near the van Hove singularity (VHS) in both intermediate (3.5 to 4 degree) and large (around 5 degree) angle twisted WSe2. The fast-propagating mode has a large speed of about 3 km/s and is consistent with a Goldstone mode for an IVC state, while the slow-moving mode is likely a gapped amplitude mode. They can be understood as the spin-valley analogues of collective modes of a superfluid, whose propagation is imaged for the first time in a condensed matter system. Our study demonstrates a powerful new approach for probing charge-neutral modes in quantum materials and offers key insights into the interplay between charge and spin-valley physics in moire superlattices.

cond-mat.mes-hall↗