Publications

Quantum circuit simulation asks how to represent the exponentially large wavefunction generated by entanglement, magic, and non-diagonal branching. A neural statebank stores each circuit layer as an autoregressive Transformer checkpoint trained from local gate updates, achieving about 10^-2 infidelity for 34-qubit long-range circuits with only 0.3 million parameters. This provides an accurate, memory-efficient approach for verifying quantum processors and simulating diverse circuit families.

Whether a Laughlin anyon fluid can turn into a topological superconductor is answered for the one-third fractional Chern insulator using a U(3) infrared parton theory in which three charge e/3 constituents build the electron and constituent pairs build a gauge-invariant charge 2e Cooper pair. The theory organizes three superconducting descendants distinguished by their neutral color response, an SC* retaining the parent Laughlin order, a chiral topological superconductor with chiral central charge 3/2, and a strong-pairing anyon superconductor, alongside a nearby zero-Hall-conductance charge density wave, with the 3/2 state also reachable by pairing a chargon metal away from commensuration. This unifies the experimentally adjacent FCI, re-entrant charge order, and chiral superconductivity of twisted MoTe2 in a single gauge-theoretic framework.

Anyons in fractional Chern insulators are not just topological labels but mobile quasiparticles whose dispersion controls the fate of the doped anyon gas, including possible superconductivity. This work shows that tunneling probes can measure that motion: quasiparticle-interference patterns in scanning tunneling spectroscopy trace the dispersion of fractionalized constituents, while momentum-conserving tunneling in quantum twisting microscopy converts continuum thresholds of the electron spectral function into anyon dispersions. The resulting spectra cleanly distinguish compact electron-like excitations, bound anyon molecules, and the unbound anyon continuum, giving experimentalists a direct window on anyon dynamics.

Van Hove singularities amplify interactions, and in a topological flat band they can seed magnetism intertwined with band geometry. Transport and magnetic circular dichroism on 4.8-degree twisted bilayer MoTe2 reveal a spontaneous anomalous Hall hot spot near filling minus one when a van Hove singularity is gate-tuned to the Fermi level, arising from an intervalley-coherent antiferromagnet that cants with doping, develops a finite-field topological Hall component consistent with a noncoplanar spin texture, and ultimately gives way to a Chern insulator. Tunable van Hove singularities in moire topological bands thus provide a route to chiral magnetism and engineered topological transitions.

Boundary criticality of the O(N) Wilson-Fisher fixed points includes the subtle extraordinary-log universality class, whose direct microscopic characterization has been difficult. Realizing the O(2) and O(3) fixed points on a fuzzy-sphere bilayer Heisenberg model, the state-operator correspondence yields boundary operator spectra, OPE coefficients, and boundary central charges for both normal and ordinary boundary conditions, with universal one- and two-point amplitudes matching Monte Carlo benchmarks and a positive extraordinary-log exponent for both N=2 and N=3. This extends fuzzy-sphere conformal spectroscopy beyond Ising to continuous symmetries and provides independent microscopic evidence for extraordinary-log boundary criticality.

The interactions among anyons decide whether a doped fractional quantum Hall state becomes a Wigner crystal, a superconductor, or an anyon gas. Segment DMRG on infinite cylinders computes charged-excitation energies in gate-screened Laughlin, Jain 2/5, and anti-Pfaffian states, finding that screening exposes an intermediate-range attraction, encoded in the oscillatory density tail of the fundamental anyon, that binds like-charged anyons into molecules with strong dependence on filling, gate distance, and fusion channel, including a charge e/2 molecule fused into the psi channel on the hole side of the anti-Pfaffian. Anyon molecules reshape expectations for addition spectra, interferometry, crystallization, and anyon superconductivity in gated devices.

Which many-body wavefunctions neural quantum states can represent efficiently remains poorly understood. This work introduces Walsh complexity, a measure of how broadly a state spreads over parity patterns, proves that shallow additive networks with tame activations cannot generate near-uniform Walsh spectra, and exhibits a simple dimerized state, preparable by one layer of controlled-Z gates and short-range entangled, whose Walsh complexity is nonetheless maximal. Numerical fits confirm that representing it requires depth growing logarithmically with system size or saturating activations, establishing an expressibility axis complementary to entanglement for variational network design.

Whether like-charged anyons can bind is central to the phase structure of doped fractional quantum Hall systems. A geometric quantization approach working entirely within the anyon Hilbert space, built from a Monte Carlo computable electrostatic potential and a Kahler potential encoding the Berry phase, shows that Laughlin quasiholes with screened Coulomb repulsion form bound pairs once the screening length approaches the magnetic length, a binding driven purely by Berry-phase effects from the oscillatory quasihole density tail. As screening increases, a sequence from free e/3 anyons through 2e/3 pairs to charge-e clusters emerges, with direct implications for charge imaging and the phase diagram of itinerant anyons in fractional Chern insulators.

Ferrofluid surfaces support two classic instabilities, the static Rosensweig peak lattice and parametric Faraday waves, but their fate under a purely oscillatory field with zero mean had not been mapped. Systematic scans of frequency and amplitude reveal two robust branches, a Faraday square-lattice regime and a Rosensweig-like peak regime, with a Faraday onset scaling near the square root of frequency, a frequency-independent peak onset at low viscosity, and a lattice wavevector growing linearly with frequency, all captured by a surface-wave theory. The phase diagram shows how AC driving alone can summon static-looking Rosensweig peaks, unifying the two canonical instabilities in one framework.

Quantum Hall edge modes are textbook chiral channels, yet how electron interactions restructure them microscopically had never been directly seen. Scanning tunneling microscopy of pristine, electrostatically defined edges in graphene images the internal structure of integer and fractional edge channels on magnetic and atomic length scales, showing interactions renormalize edge velocities, set the spacing of copropagating modes, and induce an edge valley polarization different from the bulk, with clear breakdowns of mean-field theory and chiral Luttinger liquid spectroscopy at fractional fillings. The work establishes STM as a direct probe of interacting edge physics for the expanding family of two-dimensional topological phases.

Charged anyons in a quantum Hall fluid cannot disperse, but neutral ones can, opening a richer landscape of daughter states at finite density. In quantum Hall bilayers of two Laughlin one-third states, the minimal interlayer exciton carries fractional statistics, and condensing a finite density of these anyonic excitons produces an exciton superfluid stitched to a specific bulk topological order, the neutral analogue of anyon superconductivity, most robust near the transition to the Halperin (112) state. Chern-Simons QED3 analysis of these transitions predicts an anomalously large superfluid stiffness scaling as the square root of layer imbalance and widespread composite-Fermi-surface-driven spatial symmetry breaking, all testable with existing counterflow techniques.

Combining intrinsic topological order with a gapless Goldstone mode in one phase is a longstanding goal of many-body physics. DMRG and Chern-Simons field theory show that a quantum Hall trilayer at one-third filling per layer, tuned only by the interlayer distance, hosts an intermediate 'anyon-exciton condensate' between the small-distance exciton condensate and the decoupled Laughlin limit: neutral bi-excitons condense while a 2/3 Laughlin topological order survives. The phase has sharp experimental fingerprints, vanishing double-counter-flow resistance and a layer-resolved Hall resistivity of 5/2 in units of h over e squared, within reach of existing trilayer devices.

Intervalley coherent states have been proposed as a unifying correlated phase across graphene and semiconductor moire systems, but their defining feature, a charge-neutral valley Goldstone mode, had never been observed. Ultrafast spatiotemporal imaging of twisted WSe2 reveals two propagating neutral collective modes emerging near the van Hove singularity: a fast mode at about 3 km/s consistent with the intervalley-coherent Goldstone mode and a slower mode likely its gapped amplitude partner, the spin-valley analogues of superfluid collective modes. This is the first real-space imaging of collective-mode propagation in a condensed matter system and a new window on neutral excitations in flatband materials.

Fractional Chern insulators and spin-valley-polarized superconductors appear side by side in twisted MoTe2 and rhombohedral graphene, hinting that melting a fractionalized insulator can produce pairing among fully polarized, repulsive electrons. DMRG on spinless lowest-Landau-level electrons with a tunable periodic potential shows that as the FCI gap closes, a chiral f-wave superconductor and a root-3 charge density wave emerge nearly degenerate, mirroring the observed superconducting and re-entrant integer quantum Hall phases, with the superconducting dome robust to Coulomb interactions, doping, and lattice geometry. The work predicts a superconducting dome in larger-angle twisted MoTe2 at filling 2/3 that a magnetic field should convert into a re-entrant quantum Hall state.

The conjectured continuous transition between the bosonic Laughlin state and a superfluid is a paradigmatic Landau-forbidden critical point, proposed to be described by QED3-Chern-Simons theory whose stability had been uncertain. Infinite-cylinder DMRG on half-filled bosons in the lowest Landau level with a lattice potential finds a single continuous transition where adiabatic flux insertion exposes massless Dirac quasiparticles and three lattice-related density modes share one critical exponent, evidencing an emergent SO(3) symmetry. The joint observation of Dirac dispersion and symmetry enlargement provides the first microscopic support for a stable QED3-Chern-Simons fixed point, with a numerical blueprint applicable to moire and cold-atom platforms.

Thermal Hall measurements at filling 5/2 find the half-integer quantization of the PH-Pfaffian state, while numerics consistently favor the Pfaffian or anti-Pfaffian, a decade-old contradiction at the heart of non-Abelian quantum Hall physics. Based on DMRG studies of realistic edges, this work proposes an edge reconstruction confined to the neutral Majorana sector: extra counter-propagating Majorana modes 'screen' a Pfaffian or anti-Pfaffian bulk so that its thermal transport mimics the PH-Pfaffian. The scenario requires no fine-tuning and reconciles experiment with numerics while keeping the bulk non-Abelian order intact.

The interaction-driven multicritical point of the Chern insulator to trivial insulator transition realizes Gross-Neveu-Yukawa criticality, a fermionic analogue of the Wilson-Fisher fixed point relevant to both condensed matter and high-energy physics. Exact diagonalization of Dirac fermions on the sphere sidesteps the parity anomaly and exploits full rotational symmetry, so that operator scaling dimensions can be read off directly from the excitation spectrum via the state-operator correspondence. Modest system sizes already reproduce conformal bootstrap predictions and uncover previously uncharacterized higher primary operators, establishing spherical regularization as a powerful spectroscopy of interacting Dirac criticality.

Shot noise in quantum point contacts probes the charge and tunneling statistics of quantum Hall edge excitations, provided the constriction itself is well understood. Measurements on a graphene point contact at high field reveal a 50-100 percent noise enhancement, traced to a quantum dot that forms at the saddle point when confinement competes with electron interactions, correlating the tunneling of charges. The result shows the electrostatic environment of graphene constrictions can dominate noise signatures, an essential caution for fractional-charge and anyon-statistics measurements.

Entropy is a uniquely sensitive thermodynamic probe of strongly correlated Landau levels but is notoriously hard to measure. Using the Maxwell relation between the temperature derivative of the chemical potential and the density derivative of the entropy, high-resolution chemical potential measurements on monolayer and bilayer graphene track the entropy from 300 K down to 200 mK, resolving the sequential onset of quantum Hall ferromagnetism, fractional quantum Hall states, and charge order. Excess low-temperature entropy near the even-denominator states in bilayer graphene is discussed as a possible signature of non-Abelian quasiparticle degeneracy.

Charge distribution encodes dielectric response, charge order, and fractionalization, but existing local sensing techniques lack the combined energy and spatial resolution to exploit it in quantum Hall systems. A new architecture reads out the local chemical potential of a sample through scanning tunneling spectroscopy of a proximitized detector layer, achieving sub-0.3-meV and sub-10-nm resolution, an order of magnitude beyond prior work, and resolves thermodynamic gaps and spatially oscillating screening responses of graphene quantum Hall liquids consistent with composite Fermi liquid behavior near half filling. The technique opens a path to mapping moire potentials, Wigner crystals, and individual fractional charges.

Axion electrodynamics is predicted in magnetic topological insulators, but dynamical axion signatures have eluded detection because the bulk magnetic exchange gap pins the axion field to small variations. This work identifies the material surface, where the bulk gap closes, as the natural place to look: order-one axion fluctuations survive there, and a perturbative calculation of axion-to-two-photon decay predicts an in-plane microwave photon flux orders of magnitude larger than any bulk contribution, within reach of modern microwave detection. Concrete material platforms and signal-to-noise strategies are laid out for a first observation of condensed-matter axion dynamics.

Beyond the thermal and electric Hall conductivities, fermionic fractional quantum Hall states carry 'higher' Hall conductivities that obstruct symmetry-preserving gapped edges. This work shows these invariants are encoded in the expectation value of a partial rotation combined with a U(1) phase rotation, evaluated on a single bulk wavefunction and verified numerically on Laughlin and Moore-Read states. Together with topological entanglement entropy this fully decides edge gappability for Abelian topological orders with charge conservation, extending single-wavefunction diagnostics into the symmetry-enriched domain and yielding Lieb-Schultz-Mattis-type spectral constraints.

The anomalous Hall crystal, a state that spontaneously breaks both time-reversal and continuous translation symmetry while forming a Chern band, emerged from studies of rhombohedral multilayer graphene, but the mechanism behind its stability was unclear. A minimal three-patch model, built from wavefunctions at high-symmetry points of the folded Brillouin zone, isolates two quantum-geometric phases that control the competition, predicting the topological crystal beats the trivial Wigner crystal over a wide parameter range in quantitative agreement with full Hartree-Fock calculations. The model distills the essential ingredients for interaction-generated Chern bands, making the mechanism portable to other platforms.

Quantum point contacts are the workhorse of mesoscopic quantum Hall devices, yet electron-electron interactions can qualitatively alter their behavior. Transport through a gate-defined constriction in monolayer graphene reveals Coulomb-blockaded resonances from a state localized exactly at the electrostatic saddle point, a classically unstable location, and a self-consistent Thomas-Fermi analysis shows such zero-dimensional localization is generic whenever the confinement is soft compared to the Coulomb energy. This is a direct demonstration of Coulomb-driven edge reconstruction, a key consideration for anyon interferometry in graphene devices.

Most work on twisted MoTe2 has focused on the topological states below one hole per moire cell, leaving the higher-filling phase diagram largely unexplored. A continuum model built from first-principles input, combined with self-consistent Hartree-Fock, surveys the interaction-driven states at higher integer fillings and finds valley-polarized states at odd fillings, intervalley-coherent states at even fillings, and a Chern insulator at filling two whose origin is analyzed in detail. The predicted competition among these orders provides concrete experimental signatures for the growing set of measurements above unit filling.

Wigner's electron crystal had been inferred in many two-dimensional systems but never directly visualized in its spontaneously formed state. Scanning tunneling microscopy of Bernal bilayer graphene in the lowest Landau level images a triangular-lattice Wigner crystal with the expected lattice constant, tracks its melting into a modulated liquid with increasing density or temperature, and reveals an unexpected transition to an anisotropic stripe phase at low field, with site-resolved signatures suggestive of zero-point lattice motion. Direct imaging of the crystal, its symmetry, and its melting gives a long-sought experimental window on the interplay of Coulomb crystallization, quantum fluctuations, and fractional quantum Hall competition.

Fractional quantum Hall states were observed in rhombohedral pentalayer graphene at zero magnetic field under strong displacement fields where the moire potential is weak, posing the puzzle of what stabilizes the required Chern band. Self-consistent Hartree-Fock on the interacting model finds a robust, flat, isolated Chern-one band with good quantum geometry that survives even with the moire potential switched off, and exact diagonalization plus DMRG confirm fractional quantum anomalous Hall states at partial filling. This identifies a new phase, the anomalous Hall crystal, in which interactions spontaneously break continuous translation symmetry while generating the topological band, providing a general mechanism for zero-field fractionalization in rhombohedral graphene.

Fractional quantum Hall quasiparticles are usually detected through transport, which averages over the sample and misses their spectroscopic structure. High-resolution scanning tunneling spectroscopy on ultraclean Bernal bilayer graphene resolves the sharp excitations predicted when a tunneling electron fractionalizes into bound quasiparticle states, and finds energy gaps for candidate non-Abelian even-denominator states five times larger than in semiconductor heterostructures, along with previously unobserved fractional states. The results establish bilayer graphene as an exceptionally favorable platform for manipulating non-Abelian anyons toward topological qubits.

The even-denominator fractional quantum Hall state in bilayer graphene is a leading candidate for a non-Abelian Pfaffian phase, but its energetics had not been quantitatively pinned down. Thermally activated transport gives a 5.1 K gap at 12 T for the half-filled N=1 Landau level, consistent with DMRG predictions for the Pfaffian, while direct chemical potential measurements give a thermodynamic gap of 11.6 K, about half the clean-limit theory, a discrepancy explained by a Wigner crystal of fractional quasiparticles in long-wavelength disorder. These measurements quantitatively establish bilayer graphene as a robust platform for manipulating non-Abelian anyons.

Twisted transition metal dichalcogenide homobilayers host flat topological bands whose interplay with interactions produces magnetism and quantum anomalous Hall states. Hartree-Fock calculations on the continuum model of twisted MoTe2 and WSe2 map out displacement-field-driven transitions in both topology and magnetic order, and the computed magnon spectra show that band topology amplifies the easy-axis anisotropy, yielding magnon gaps up to 7 meV that protect two-dimensional ferromagnetism against thermal fluctuations. The results tie the thermal robustness of the observed anomalous Hall states directly to their band topology.

Microwave impedance microscopy images topological edge states, but interpreting its signal on quantum materials has relied on classical lumped-element circuits of limited validity. This work builds a general linear-response theory of the MIM signal and applies it to Chern insulators, predicting an enhanced edge response from collective edge magnetoplasmon modes whose resonance frequency encodes the Chern number and sample circumference, in agreement with measurements on a Cr-doped (Bi,Sb)2Te3 quantum anomalous Hall device. The framework turns MIM into a quantitative probe that can extract topological invariants and distinguish topological from trivial edge conduction.

Electrical switching of magnetic order is a central goal of spintronics, and crystalline graphene multilayers offer a new venue: their correlated ground states carry spin and valley polarization. This proposal shows that Bernal bilayer or rhombohedral trilayer graphene encapsulated by transition metal dichalcogenides acquires proximity-induced spin-orbit coupling that ties the isospin polarization to the displacement field, so reversing a gate voltage deterministically switches spin and/or valley order, as substantiated by Hartree-Fock calculations. Selective switching of distinct isospin flavors via gate and substrate alignment makes these heterostructures a promising all-electrical platform for spintronics and valleytronics.

Whether a two-dimensional topologically ordered phase admits a gapped edge is not fully determined by its chiral central charge, since 'higher central charges' provide further obstructions. This work shows the higher central charges can be extracted from a single ground-state wavefunction as the expectation value of a partial rotation operator, verified on the bosonic Laughlin state and the non-Abelian phase of the Kitaev honeycomb model, thereby completely determining edge gappability for Abelian bosonic topological orders. The construction also yields Lieb-Schultz-Mattis-type constraints on bulk-boundary spectra and is directly implementable on quantum simulators.

Chiral Luttinger liquid theory predicts a universal, quantized power-law suppression of tunneling into fractional quantum Hall edges, a hallmark that had resisted clean experimental confirmation. Conductance measurements across a graphene point contact bridging integer and fractional edges reveal the predicted universal quadratic temperature and voltage scaling at weak coupling, and at strong coupling perfect Andreev reflection of fractionalized quasiparticles saturates the conductance at half a conductance quantum. The strong-coupling regime realizes a nearly dissipationless DC voltage step-up transformer whose gain of 3/2 stems directly from charge fractionalization.

Two-dimensional tensor network simulation of fermions is hampered by the computational cost of contracting general PEPS networks. This work generalizes isometric tensor network states to fermionic systems, enabling efficient 2D adaptations of one-dimensional algorithms, and benchmarks a time-evolution block-decimation scheme that captures ground states of gapped, Dirac, and chiral-edge systems as well as real-time fermion scattering and edge dynamics of a Chern insulator. The formalism provides a scalable, well-conditioned variational class for correlated fermions in two dimensions.

Hole-doped rhombohedral trilayer graphene shows correlated metals and superconductivity near van Hove singularities, where the diverging density of states amplifies interaction effects. A hot-spot model resolving the displacement-field-tunable Fermi surface nesting, combined with an unbiased renormalization group analysis, finds instabilities toward intervalley coherent metals and spin-singlet d-wave or i-wave superconductivity depending on the field, with realistic Coulomb repulsion plus a ferromagnetic intervalley Hund's coupling sufficient to explain the phase diagram. The analysis indicates phonons are largely irrelevant here, in sharp contrast to twisted graphene multilayers.

Electrostatic control on sub-100-nanometer scales in ultraclean van der Waals devices has been a longstanding fabrication bottleneck because conventional lithography contaminates the heterostructure. This work introduces a resist-free local anodic oxidation technique for patterning graphite gates, demonstrated with a graphene quantum point contact that shows chiral Luttinger liquid tunneling in the fractional quantum Hall regime and in-situ tunable edge confinement. The method paves the way toward anyon-scale control and coherent edge-state interferometry in fractional quantum Hall devices.

Superconductivity in rhombohedral trilayer graphene appears next to a metallic phase with reduced isospin symmetry, raising the question of whether the symmetry breaking drives the pairing. Combining Hartree-Fock analysis with experimental constraints, this work identifies the neighboring order as intervalley coherence and shows that its fluctuations can act as a pairing glue, producing chiral unconventional superconductivity, with the intervalley Hund's coupling selecting singlet pairing from an unpolarized normal state. This established intervalley-coherence fluctuations as a leading candidate mechanism for superconductivity in crystalline graphene multilayers.

Rotational misalignment of the top layers of a topological insulator imprints a moire superlattice on its Dirac surface states, which cannot form isolated flat bands because of their anomaly-protected topology. Instead, the moire potential generates high-order van Hove singularities with power-law divergent density of states, and phonon-mediated pairing at these singularities yields a superconducting transition temperature with anomalously strong power-law dependence on the coupling. Moire engineering of TI surfaces thus offers a tunable route to enhanced superconductivity in a spin-momentum-locked electron system.

Mott insulators built from topologically obstructed bands lack exponentially localized Wannier orbitals, so the usual superexchange framework for quantum magnetism does not directly apply. This work develops a strong-coupling theory in which electrons singly occupy localized but nonorthogonal orbitals, and shows diagrammatically that the nonorthogonality generates new spin-exchange channels that stabilize ferromagnetism up to a finite bandwidth set by the orbital overlap. The mechanism explains the robust ferromagnetism seen in Chern and fragile-topological flat bands and opens a route to frustrated magnetism near the ferromagnet-antiferromagnet crossover.

Fracton phases host excitations with restricted mobility, and 'foliated' fracton order organizes them by treating stacks of 2D topological layers as a renormalization resource. This work proves the Majorana checkerboard model has foliated fracton order by constructing an exact local unitary mapping to the semionic X-cube model plus decoupled fermionic modes, using toric code layers in an entanglement renormalization scheme. The result places a paradigmatic Majorana fracton model firmly within the X-cube foliated phase, sharpening the classification of fracton orders.