arXiv subjects

Ahmed Abouelkomsan

Publications and source records attributed to Ahmed Abouelkomsan.

At least 19 recordsLinked to original sources

arXiv2026

Non-Abelian quantum Hall states at strong Landau level mixing: finding anyons with first-principles AI

Non-Abelian anyons, strange particles forming the basis of fault-tolerant topological quantum computing, are predicted to emerge in fractional quantum Hall states at even-denominator filling factors. Identifying which topological order is realized has proven to be a challenging problem that requires an accurate, non-perturbative treatment of realistic Landau level mixing, which has so far been missing from theoretical studies. Here we present the first complete solution of non-Abelian quantum Hall problem that includes all electrons and all Landau levels, for spin-polarized electrons at filling factor $ν= 3/2$. We develop a momentum-resolved neural-network variational wave function, optimized solely on the microscopic Hamiltonian, which gives direct access to the topologically degenerate ground states. Without any physics input about the expected outcome, it discovers a degenerate ground-state manifold whose entanglement reveals anyons with quantum dimension $\sqrt{2}$, the hallmark of Ising-type non-Abelian order. By directly computing the overlap with trial wave functions, we further show that Landau level mixing favors the anti-Pfaffian over other candidate states. Our results demonstrate the power of neural-network wave functions in finding and characterizing non-Abelian anyons from first principles, in regimes of strong Landau level mixing, relevant to many recent experiments.

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arXiv2026

Quantization through dissipation: impurity states and the optical quantum Hall effect

The integer quantum Hall effect remains the most paradigmatic and remarkable example of exact quantization in condensed matter physics. Its Hall conductivity $σ_{xy}$ is fixed to $e^2/h$ times an integer to a precision limited only by measurement and independent of disorder or interactions. This robustness has several explanations, each capturing a strikingly different piece of the physics. In Laughlin's gauge argument, flux insertion pumps an integer charge between edges, so quantization follows from gauge invariance alone. The edge-channel picture instead attributes transport to chiral, ballistic 1D channels at the sample boundary, one per filled Landau level. Bulk arguments tie $σ_{xy}$ to a topological invariant of the disordered system, with extended states compensating exactly for the current not carried by localized ones. Here we demonstrate an additional route to understanding quantization, rooted in the finite-frequency dissipative electrodynamics of the bulk. Using high-precision terahertz Faraday rotation and numerics, we show that the cyclotron resonance alone does not give quantized plateaus under Kramers-Kronig transformation. Quantization is recovered only once a faint, low-frequency, topologically enforced dissipative contribution from impurity states is included. This dynamical mechanism, hiding in plain sight within the dissipative response, ties the DC value to the finite-frequency optical response and offers a new route to quantization through the optical Hall effect, complementary to previous pictures.

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arXiv2026

Shining light on collective modes in moiré fractional Chern insulators

We show that collective excitations and optical responses of moiré fractional Chern insulators (FCIs) drastically differ from those of standard fractional quantum Hall (FQH) states in a Landau level. By constructing a variational wavefunction that incorporates the moiré lattice effect, we capture the collective modes in FCIs across a range of crystal momenta including the roton minimum. Interestingly, new collective modes are found in the long wavelength limit ($\boldsymbol{q} \rightarrow 0$) at low energy below the excitation continuum, distinct from the FQH case. Some of these modes are optically active and manifest as sharp peaks in optical conductivity at THz frequency. We further show that intraband optical absorption and spectral weight in twisted ${\rm MoTe}_2$ are highly tunable by the displacement field. Our work thus establishes optical spectroscopy as a powerful tool to illuminate the unique collective modes of moiré FCIs.

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arXiv2026

Zoology of chiral superconductors in Chern bands

Evidence for chiral superconductivity has recently been observed in several van der Waals systems including rhombohedral multilayer graphene and twisted bilayer MoTe$_2$. In the latter, superconductivity emerges at carrier densities near a fractional Chern insulator. This raises the question of what kinds of superconductors may emerge in a system of electrons in a topological band with strong repulsive interactions. Here, we adapt the target-phase optimization method to search for chiral superconductors in a minimal model of interacting electrons in a Chern band. We construct a differentiable loss function for superconductors from the sign oscillation of the pair-binding energy and combine gradient-based optimization with a rigorous screening procedure to identify and characterize superconductors. Applying this framework within exact diagonalization to spinless electrons in periodically modulated Landau levels with screened Coulomb interactions, we uncover a broad family of chiral superconducting phases. At filling $ν=2/3$, we recover the previously identified $f-\mathrm{i} f$ hole superconductors and find additional $p\pm \mathrm{i} p$ and $f+\mathrm{i} f$ superconductors of both electrons and holes, occurring near and far from the limit of ideal quantum geometry. At $ν=1/2$, we identify $p- \mathrm{i} p$ electron and $f-\mathrm{i} f$ hole superconductors and find, for the first time, a direct transition between chiral superconductors and composite Fermi liquids. Our results reveal that chiral superconductivity in Chern bands comprises a diverse landscape of competing pairing instabilities and establish target-phase optimization as a general strategy for searching for quantum phases in complex interacting systems.

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arXiv2026

First-Principles AI finds crystallization of fractional quantum Hall liquids

When does a fractional quantum Hall (FQH) liquid crystallize? Addressing this question requires a framework that treats fractionalization and crystallization on equal footing, especially in strong Landau-level mixing regime. Here, we introduce MagNet, a self-attention neural-network variational wavefunction designed for quantum systems in magnetic fields on the torus geometry. We show that MagNet provides a unifying and expressive ansatz capable of describing both FQH states and electron crystals within the same architecture. Trained solely by energy minimization of the microscopic Hamiltonian, MagNet discovers topological liquid and electron crystal ground states across a broad range of Landau-level mixing. Our results highlight the power of first-principles AI for solving strongly interacting many-body problems and finding competing phases without external training data or physics pre-knowledge.

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arXiv2026

Rhombohedral Graphene: A Tale of Many Crystals

Experiments on rhombohedral graphene have uncovered an extraordinary wealth of correlated quantum phases - from chiral superconductors to electronic crystals - all within a single family of atomically thin materials. Here, we introduce a simple indicator, derived from the noninteracting band dispersion, that identifies strongly correlated regions in the phase diagram of rhombohedral graphene as a function of carrier density and displacement field. We develop a neural-network variational Monte Carlo method, combined with Hartree-Fock theory, to solve the interacting ground states. Our calculation reveals a variety of electron crystals with no classical analog. These include, at increasing density: Wigner crystal, self-doped Wiger crystal, as well as ''anticrystal'', a lattice of holes in an electron liquid. We discuss their experimental manifestations and possible connection to superconductivity.

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arXiv2026

Scaling universal Fermi network toward ground states: A diffusion-Monte-Carlo assessment

In this work, we show that Fermi Sets---a provably universal neural network architecture for fermionic wavefunctions---can be systematically scaled up to find interacting ground states through energy minimization in a variational Monte Carlo framework. By further performing fixed-phase diffusion Monte Carlo (DMC) on the optimized neural network wavefunction, we demonstrate that as the network size increases, the variational energy systematically decreases while the energy improvement from DMC collapses monotonically to zero, indicating convergence to the ground state. We illustrate the scaling of Fermi Sets accompanied by the DMC assessment for interacting electrons in jellium and in a quantum dot under high magnetic fields.

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arXiv2026

Topological Order in Neural Wavefunctions

Topologically ordered states are among the most interesting quantum phases of matter that host emergent quasi-particles having fractional charge and obeying fractional quantum statistics. Theoretical study of such states is however challenging owing to their strong-coupling nature that prevents conventional mean-field treatment. Here, we demonstrate that an attention-based deep neural network provides an expressive variational wavefunction that discovers fractional Chern insulator ground states purely through energy minimization without prior knowledge and achieves remarkable accuracy. We introduce an efficient method to extract ground state topological degeneracy -- a hallmark of topological order -- from a single optimized real-space wavefunction in translation-invariant systems by decomposing it into different many-body momentum sectors. Our results establish neural network variational Monte Carlo as a versatile tool for discovering strongly correlated topological phases.

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arXiv2026

Anti-topological crystal and non-Abelian liquid in twisted semiconductor bilayers

We show that electron crystals compete closely with non-Abelian fractional Chern insulators in the half-filled second moiré band of twisted bilayer MoTe$_2$. Depending on the twist angle and microscopic model, these crystals can have non-zero or zero Chern numbers $C$. The $C=0$ crystal occurs because contributions to the total Chern number from the full first band (+1) and half-full second band (-1) cancel. This is counterintuitive because the first two non-interacting bands in a given valley have the same Chern number $+1$. For these two reasons, we call this crystal an anti-topological crystal. The anti-topological crystal is a novel type of electron crystal that may occur in systems with multiple Chern bands at filling factors $n>1$.

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arXiv2026

Topological superconductivity with emergent vortex lattice in twisted semiconductors

The coexistence of superconductivity and fractional quantum anomalous Hall (FQAH) effect has recently been observed in twisted MoTe$_2$ and theoretically demonstrated in a model of repulsively interacting electrons under an emergent magnetic field arising from the layer pseudospin texture in moiré superlattice. Here, we show that this superconducting state is a chiral $f$-wave superconductor hosting an array of $double$ vortices, which are induced by the emergent magnetic field with $h/e$ flux quanta per moiré unit cell. This superconducting vortex lattice state is topological and features Chern number $-1/2$, giving rise to a half-integer thermal Hall conductance. Our theory provides a common mechanism and unified understanding of FQAH and topological superconductivity, with a rich phase diagram controlled by the spatial modulation of the emergent magnetic field.

cond-mat.supr-con↗

arXiv2025

From Fractionalization to Chiral Topological Superconductivity in a Flat Chern Band

We show that interacting electrons in a flat Chern band can form, in addition to fractional Chern insulators, a chiral $f$-wave topological superconductor that hosts neutral Majorana fermion edge modes. Superconductivity emerges from an interaction-induced metallic state that exhibits anomalous Hall effect, as observed in rhombohedral graphene and near the $ν=\frac{2}{3}$ fractional Chern insulator in twisted transition metal dichalcogenides.

cond-mat.supr-con↗

arXiv2025

Broken Symmetry in Ideal Chern Bands

Recent observations of the fractional anomalous quantum Hall effect in moiré materials have reignited the interest in fractional Chern insulators (FCIs). The chiral limit in which analytic Landau level-like single-particle states form an ``ideal" Chern band and local interactions lead to Laughlin-like FCIs at $1/3$ filling, has been very useful for understanding these systems by relating them to the lowest Landau level. We show, however, that, even in the idealized chiral limit, a fluctuating quantum geometry is associated with strongly broken symmetries and a phenomenology very different from that of Landau levels. In particular, particle-hole symmetry is strongly violated and e.g. at $2/3$ filling an emergent interaction driven Fermi liquid state with no Landau level counterpart is energetically favoured. In fact, even the exact Laughlin-like zero modes at $1/3$ filling have a non-uniform density tracking the underlying quantum geometry. Switching to a Coulomb interaction, the ideal Chern band with electron filling of $1/4$ features trivial charge density wave states. Moreover, applying a particle-hole transformation reveals that the ideal Chern band with hole filling of $3/4$ supports a quantum anomalous Hall crystal with quantized Hall conductance of $e^2/h$. These phenomena have no direct lowest Landau level counterpart.

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arXiv2025

Compressible quantum liquid with vanishing Drude weight

We explore the possibility of quantum liquids that are compressible but have vanishing DC conductivity in the absence of disorder. We show that the composite Fermi liquid emerging from strong interaction in a generic Chern band has zero Drude weight, in stark contrast to normal Fermi liquids. Our work establishes the absence of Drude weight as the defining property of the composite Fermi liquid phase, which distinguishes it from the Fermi liquid or other types of non-Fermi liquids. Our findings point to a possibly wide class of gapless quantum phases with unexpected transport and optical properties.

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arXiv2025

Non-Abelian spin Hall insulator

Motivated by a recent experiment reporting the fractional quantum spin Hall effect in twisted ${\rm MoTe}_2$, we investigate microscopically the prospects of realizing exotic topologically ordered states beyond conventional quantum Hall physics. We show that a non-Abelian spin Hall insulator, a state of two copies of the non-Abelian Moore-Read state, can be stabilized at half filling of time-reversal conjugate Chern bands. We elucidate that the existence of this phase relies on the reduction of opposite-spin interactions at short distances to overcome the Ising ferromagnetism. Moreover, we demonstrate that band mixing provides a generic mechanism for this reduction to be achieved. Quite remarkably, we find that a renormalization of opposite-spin interactions at short distances as small as 15 % of the moiré period is sufficient for a direct transition to a completely spin unpolarized phase which supports the non-Abelian spin Hall insulator. Furthermore, we show that the non-Abelian spin Hall insulator can either break time-reversal symmetry or preserve it depending on the underlying topological order.

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arXiv2024

Non-Abelian fractionalization in topological minibands

Motivated by the recent discovery of fractional quantum anomalous Hall states in moiré systems, we consider the possibility of realizing non-Abelian phases in topological minibands. We study a family of moiré systems, skyrmion Chern band models, which can be realized in two-dimensional semiconductor-magnet heterostructures and also capture the essence of twisted transition metal dichalcogenide homobilayers. We show using many-body exact diagonalization that, in spite of strong Berry curvature variations in momentum space, the non-Abelian Moore-Read state can be realized at half filling of the second miniband. These results demonstrate the feasibility of non-Abelian fractionalization in moiré systems without Landau levels and shed light on the desirable conditions for their realization. In particular, we highlight the prospect of realizing the Moore-Read state in twisted semiconductor bilayers.

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arXiv2024

Quantum anomalous Hall crystal at fractional filling of moiré superlattices

We predict the emergence a state of matter with intertwined ferromagnetism, charge order and topology in fractionally filled moiré superlattice bands. Remarkably, these quantum anomalous Hall crystals exhibit a quantized integer Hall conductance that is different than expected from the filling and Chern number of the band. Microscopic calculations show that this phase is robustly favored at half-filling ($ν=1/2$) at larger twist angles of the twisted semiconductor bilayer $t$MoTe$_2$

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arXiv2024

Multiferroicity and Topology in Twisted Transition Metal Dichalcogenides

Van der Waals heterostructures have recently emerged as an exciting platform for investigating the effects of strong electronic correlations, including various forms of magnetic or electrical orders. Here, we perform an unbiased exact diagonalization study of the effects of interactions on topological flat bands of twisted transition metal dichalcogenides (TMDs) at odd integer fillings. For hole-filling $ν_h = 1$, we find that Chern insulator phases, expected from interaction-induced spin-valley polarization of the bare bands, are quite fragile, and give way to spontaneous multiferroic order -- coexisting ferroelectricity and ferromagnetism, in presence of long-range Coulomb repulsion. We provide a simple real-space picture to understand the phase diagram as a function of interaction range and strength. Our findings establish twisted TMDs as a novel and highly tunable platform for multiferroicity, and we outline a potential route towards electrical control of magnetism in the multiferroic phase.

cond-mat.str-el↗

arXiv2024

Band mixing in the quantum anomalous Hall regime of twisted semiconductor bilayers

Remarkable recent experiments have observed fractional quantum anomalous Hall (FQAH) effects at zero field and unusually high temperatures in twisted semiconductor bilayer $t$MoTe$_2$. Intriguing observations in these experiments such as the absence of integer Hall effects at twist angles where a fractional Hall effect is observed, do however remain unexplained. The experimental phase diagram as a function of twist angle remains to be established. By comprehensive numerical study, we show that band mixing has large qualitative and quantitative effects on the energetics of competing states and their energy gaps throughout the twist angle range $θ\leq 4^\circ$. This lays the ground for the detailed realistic study of a rich variety of strongly correlated twisted semiconductor multilayers and an understanding of the phase diagram of these fascinating systems.

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