arXiv subjects

Gil Young Cho

Publications and source records attributed to Gil Young Cho.

At least 19 recordsLinked to original sources

arXiv2026

Wavefunctions for Anyon Superconductors

Anyon superconductivity arises from the condensation of mobile anyons rather than from a conventional Cooper instability, yet a systematic wavefunction description remains lacking. We develop a hierarchy-wavefunction construction for superconducting states derived from parent topological orders and identify their off-diagonal long-range order, condensate charge, chiral central charge, and residual topological order through the plasma analogy and topological field theories. We construct Abelian and non-Abelian examples descending from the semion state, a $\nu=2/3$ hierarchy state, the $\nu=1/3$ Laughlin state, $\nu=1$ integer quantum Hall state, and Pfaffian state. Remarkably, for the semion case, the superconducting many-semion wavefunction is equivalent to a state of fermionized anyons filling two effective Landau levels, recovering Laughlin's original construction of semion superconductor. Finally, we show that hierarchy wavefunctions emerge naturally in the dilute, long-distance limit of the anyon-Hilbert-space formulation, which applies to ideal Chern bands and moir\'e bands of twisted bilayer MoTe$_2$. Our results establish a unified wavefunction-level framework linking anyon condensation, superconducting order, and topological field theory.

cond-mat.str-el↗

arXiv2026

Quaternionic Hermitian Band Geometry in Four Dimensions: Realization on $S^4$ and Obstruction on $T^4$

We establish a realization-obstruction dichotomy for quaternionic Hermitian band geometry in four-dimensional parameter spaces: the minimal-charge lowest Landau level on $S^{4}$ provides a global realization, whereas an everywhere nondegenerate saturated realization induced by a single occupied quaternionic band is obstructed on $T^{4}$. An antiunitary symmetry $\mathcal{J}$ satisfying $\mathcal{J}^{2}=-1$ makes the occupied doublet a quaternionic band. Within this setting, we formulate the quaternionic Wirtinger inequality as a band-geometric bound involving the quantum metric and the second Chern density. At every nondegenerate saturation point, the canonical geometry of the quaternionic projective space pulls back to a compatible quaternionic structure on the parameter space; if these conditions hold everywhere, the parameter space acquires quaternionic Hermitian band geometry. On $S^{4}$, we express the minimal-charge states as quaternionic Perelomov coherent states and establish everywhere nondegenerate saturation, thereby realizing quaternionic Hermitian band geometry. On $T^{4}$, by contrast, a minimal four-band system saturates the inequality everywhere, but topology forces the quantum metric to become degenerate somewhere, obstructing a globally induced quaternionic structure. An explicit lattice Dirac Hamiltonian exhibits this obstruction. Adding unoccupied bands cannot remove this obstruction when the inequality is saturated everywhere, since the image of any nondegenerate saturated projector remains confined to a fixed $\mathbb{H}P^{1}$. These results provide a symmetry-aware framework for non-Abelian band geometry and show how parameter-space topology constrains the global realization of quaternionic Hermitian band geometry.

cond-mat.mes-hall↗

arXiv2026

Three-Dimensional Non-Foliated Fractional Quantum Hall Phases with Irrational Anyons in Twisted van der Waals Multilayers

Three-dimensional fractional quantum Hall phases offer a route to intrinsically higher-dimensional topological order beyond simple stacks of two-dimensional quantum Hall liquids. Such phases can exhibit non-foliated, intrinsically three-dimensional entanglement structures, exponentially large topological degeneracies and quasiparticles with irrational braiding statistics. Their microscopic realization has remained elusive because Landau quantization in three dimensions generally leaves dispersive one-dimensional bands, favoring metallic and density-wave states over incompressible fractional liquids. Here we show that large-angle twisted van der Waals multilayers provide a practical route around this obstruction. Large twist angles suppress coherent interlayer tunneling through momentum mismatch, while the atomic-scale layer separation preserves strong interlayer Coulomb interactions. Using Monte Carlo calculations to compare the energies of an extensive set of 862 competing trial wavefunctions, we find that generalized Halperin states with quantum coherence extending across multiple consecutive layers are stabilized. In experimentally accessible magnetic-field regimes, these states replace the metallic spontaneous-interlayer-coherent phases that dominate conventional untwisted graphite-like multilayers. The resulting liquids realize non-foliated fractional quantum Hall order closely related to fractonic topological order, hosting quasiparticles with rational electric charges but irrational braiding statistics. Their large topological degeneracy and non-rational statistical phases may offer unconventional resources for quantum information storage and processing. Our results establish twisted van der Waals multilayers as a realistic materials platform for three-dimensional fractional Hall matter beyond conventional two-dimensional quantum Hall systems.

cond-mat.str-el↗

arXiv2026

Remote Moir\'e Modulation of Decoupled Dirac Subsystems in Twisted Trilayer Graphene

Moir\'e superlattices are generally assumed to act only at the interface where lattice mismatch or twist occurs. Here, we study charge transport in large-angle helical twisted trilayer graphene, where interlayer tunneling is strongly reduced. When only the top monolayer graphene is aligned with hBN, the electronic response reorganizes into a moir\'e-modulated monolayer and a remaining twisted bilayer graphene subsystem. Despite the absence of any explicit structural moir\'e in the twisted bilayer, we observe satellite-like features in its electronic response that run parallel to the primary spectrum and are locked to the density scale of the hBN/graphene moir\'e. These findings indicate that a moir\'e potential may not be confined to its structural interface and can, through electrostatic coupling, influence a spatially separated Dirac subsystem even in the absence of strong interlayer tunneling.

cond-mat.mes-hall↗

arXiv2026

$\mathrm{U}(2)$ Chern-Simons-Ginzburg-Landau Theory of Fractional Quantum Hall Hierarchies

We construct effective $\mathrm{U}(2)$ Chern-Simons-Ginzburg-Landau theories for Abelian and non-Abelian fractional quantum Hall hierarchies for those which had previously been described only through categorical data or trial wavefunctions. Our framework captures both Abelian hierarchy states built on half-filled Pfaffian-type parents and non-Abelian hierarchies emerging from Abelian states. It reproduces all filling fractions obtained from wavefunction and categorical constructions and, moreover, uniquely determines the corresponding topological orders. We also identify an intriguing particle-hole symmetry relating two hierarchy sequences, one built on a trivial insulator and the other on the $\nu=1$ integer quantum Hall state, which respectively generate the Read-Rezayi sequences and their particle-hole conjugates under the same hierarchy construction.

cond-mat.str-el↗

arXiv2026

A Unified Categorical Description of Quantum Hall Hierarchy and Anyon Superconductivity

We present a unified category-theoretic framework for quantum Hall hierarchy constructions and anyon superconductivity based on modular tensor categories over $\mathrm{Rep}(\mathrm{U}(1))$ and $\mathrm{sRep}(\mathrm{U}(1)^f)$. Our approach explicitly incorporates conserved $\mathrm{U}(1)$ charge and formulates doping via a generalized stack-and-condense procedure, in which an auxiliary topological order is stacked onto the parent phase, and the quasiparticles created by doping subsequently condense. Depending on whether this condensation preserves or breaks the $\mathrm{U}(1)$ symmetry, the system undergoes a transition to a quantum Hall hierarchy state or to an anyon superconductor. For anyon superconductors, the condensate charge is determined unambiguously by the charged local bosons contained in the condensable algebra. Our framework reproduces all known anyon superconductors obtained from field-theoretic analyses and further predicts novel phases, including a charge-$2e$ anyon superconductor derived from the Laughlin state and charge-$ke$ anyon superconductors arising from bosonic $\mathbb{Z}_k$ Read-Rezayi states. By placing hierarchy transitions and anyon superconductivity within a single mathematical formalism, our work provides a unified understanding of competing and proximate phases near experimentally realizable fractional quantum Hall states.

cond-mat.str-el↗

arXiv2026

Gluing Randomness via Entanglement: Tight Bound from Second R\'enyi Entropy

The efficient generation of random quantum states is a long-standing challenge, motivated by their diverse applications in quantum information processing tasks. In this work, we identify entanglement as the key resource that enables local random unitaries to generate global random states by effectively gluing randomness across the system. Specifically, we demonstrate that approximate random states can be produced from an entangled state $|\psi\rangle$ through the application of local random unitaries. We show that the resulting ensemble forms an approximate state design with an error saturating as $\Theta(e^{-\mathcal{N}_2(\psi)})$, where $\mathcal{N}_2(\psi)$ is the second R\'enyi entanglement entropy of $|\psi\rangle$. Furthermore, we prove that this tight bound also applies to the second R\'enyi entropy of coherence when the ensemble is constructed using coherence-free operations. These results imply that, when restricted to resource-free gates, the quality of the generated random states is determined entirely by the resource content of the initial state. Notably, we find that among all $\alpha$-R\'enyi entropeis, the second R\'enyi entropy yields the tightest bounds. Consequently, these second R\'enyi entropies can be interpreted as the maximal capacities for generating randomness using resource-free operations. Finally, moving beyond approximate state designs, we utilize this entanglement-assisted gluing mechanism to present a novel method for generating pseudorandom states in multipartite systems from a locally entangled state via pseudorandom unitaries in each of parties.

quant-ph↗

arXiv2025

Superconductivity Proximate to Non-Abelian Fractional Spin Hall Insulator in Twisted Bilayer MoTe$_2$

Twisted bilayer MoTe$_2$ near two-degree twists has emerged as a platform for exotic correlated topological phases, including ferromagnetism and a non-Abelian fractional spin Hall insulator. Here we reveal the unexpected emergence of an intervalley superconducting phase that intervenes between these two states in the half-filled second moir\'{e} bands. Using a continuum model and exact diagonalization, we identify superconductivity through multiple signatures: negative binding energy, a dominant pair-density eigenvalue, finite superfluid stiffness, and pairing symmetry consistent with a time-reversal-symmetric nodal extended $s$-wave state. Remarkably, our numerical calculation suggests a continuous transition between superconductivity and the non-Abelian fractional spin Hall insulator, in which topology and symmetry evolve simultaneously, supported by an effective field-theory description. Notably, our field-theoretic analysis indicates that superconductivity is driven by the condensation of charge-$e/2$ self-bosonic non-Abelian anyons, thereby providing a concrete realization of anyon superconductivity. Complementarily, when approached from the normal metallic side, superconductivity instead emerges from a Kohn-Luttinger instability enabled by the non-uniform quantum geometry of the flat moir\'{e} bands. Our results establish higher moir\'{e} bands as fertile ground for intertwined superconductivity and topological order, and point to experimentally accessible routes for realizing superconductivity in twisted bilayer MoTe$_2$.

cond-mat.str-el↗

arXiv2025

Spontaneous emission decay and excitation in photonic time crystals

Over the last few decades, the predominant strategies for controlling spontaneous emission have involved tailoring the spatial surroundings of quantum emitters or atoms to create resonant or spatially periodic photonic structures. However, the rise of time-varying photonics has prompted a reevaluation of spontaneous emission in dynamically changing environments, especially within photonic time crystals, where optical properties undergo time-periodic modulation. Here, we apply classical light-matter interaction theory together with Floquet analysis to reveal a substantial enhancement of the spontaneous emission decay rate at the momentum gap frequency in photonic time crystals. Moreover, our findings suggest that photonic time crystals enable a nonequilibrium light-matter interaction process: the spontaneous excitation of an atom from its ground state to an excited state, accompanied by the concurrent emission of a photon, referred to as spontaneous emission excitation.

physics.optics↗

arXiv2025

Correlated interlayer quantum Hall state in large-angle twisted trilayer graphene

Trilayer graphene allows systematic control of its electronic structure through stacking sequence and twist geometry, providing a versatile platform for correlated states. Here we report magnetotransport in alternating twisted trilayer graphene with a twist angle of about 5$^{\circ}$. The data reveal an electron-hole asymmetry that can be captured by introducing layer-dependent potential shifts. At charge neutrality ($\nu_{\mathrm{tot}}=0$), three low-resistance states appear, which Hartree-Fock mean-field analysis attributes to emerging spin-resolved helical edge modes similar to those of quantum spin Hall insulators. At $\nu_{\mathrm{tot}}=-1$, we also observe suppressed resistance when the middle and bottom layers are each half filled while the top layer remains inert at $\nu=-2$, consistent with an interlayer excitonic quantum Hall state. These results demonstrate correlated interlayer quantum Hall phases in alternating twisted trilayer graphene, including spin-resolved edge transport and excitonic order.

cond-mat.mes-hall↗

arXiv2025

Ferroelectric switching of interfacial dipoles in $\alpha$-RuCl$_3$/graphene heterostructure

We demonstrate electrically switchable, non-volatile dipoles in graphene/thin hBN/$\alpha$-RuCl$_3$ heterostructures, stabilized purely by interfacial charge transfer across an atomically thin dielectric barrier. This mechanism requires no sliding or twisting to explicitly break inversion symmetry and produces robust ferroelectric-like hysteresis loops that emerge prominently near 30~K. Systematic measurements under strong in-plane and out-of-plane magnetic fields reveal negligible effects on the hysteresis characteristics, confirming that the primary mechanism driving the dipole switching is electrostatic. Our findings establish a distinct and robust route to electrically tunable ferroelectric phenomena in van der Waals heterostructures, opening opportunities to explore the interplay between interfacial charge transfer and temperature-tuned barrier crossing of dipole states at the atomic scale.

cond-mat.mtrl-sci↗

arXiv2025

Most two-dimensional bosonic topological orders forbid sign-problem-free quantum Monte Carlo: Nonpositive Gauss sum as an indicator

Quantum Monte Carlo is a powerful tool for studying quantum many-body physics, yet its efficacy is often curtailed by the notorious sign problem. In this Letter, we introduce a novel criterion for the "intrinsic" sign problem in two-dimensional bosonic topological orders, which cannot be resolved by local basis transformations or adiabatic deformations of the Hamiltonian. Specifically, we find that the positivity of higher Gauss sums is a necessary condition for a two-dimensional bosonic topological order to be realized by a stoquastic Hamiltonian, and hence sign-problem-free. Equivalently, a nonpositive higher Gauss sum for a given topological order indicates the presence of an intrinsic sign problem. This condition not only aligns with prior findings but significantly broadens their scope. Using this new criterion, we examine the Gauss sums of all 405 bosonic topological orders classified up to rank 12, and strikingly find that 398 of them exhibit intrinsic sign problems. We also uncover intriguing links between the intrinsic sign problem, gappability of boundary theories, and time-reversal symmetry, suggesting that sign-problem-free quantum Monte Carlo may fundamentally rely on both time-reversal symmetry and gapped boundaries. These results highlight the deep connection between the intrinsic sign problem and fundamental properties of topological phases, offering valuable insights into their classical simulability.

cond-mat.str-el↗

arXiv2025

Pseudochaotic Many-Body Dynamics as a Pseudorandom State Generator

Quantum chaos is central to understanding quantum dynamics and is crucial for generating random quantum states, a key resource for quantum information tasks. In this work, we introduce a new class of quantum many-body dynamics, termed pseudochaotic dynamics. Although distinct from chaotic dynamics, out-of-time-ordered correlators, the key indicators of quantum chaos, fail to distinguish them. Moreover, pseudochaotic dynamics generates pseudorandom states that are computationally indistinguishable from Haar-random states. We construct pseudochaotic dynamics by embedding a smaller $k$-qubit subsystem into a larger $n$-qubit system. We demonstrate that a subsystem of size $k=ω(\log n)$ is sufficient to induce pseudochaotic behavior in the entire $n$-qubit system. Furthermore, we construct a quantum circuit exhibiting pseudochaotic dynamics and demonstrate that it generates pseudorandom states within $\mathrm{polylog}(n)$ depth. In summary, our results constitute the discovery of new quantum dynamics that are computationally indistinguishable from genuine quantum chaos, which provides efficient routes to generate useful pseudorandom states.

quant-ph↗

arXiv2025

Shallow quantum circuit for generating extremely low-entangled approximate state designs

Random quantum states have various applications in quantum information science. We discover a new ensemble of quantum states that serve as an $\epsilon$-approximate state $t$-design while possessing extremely low entanglement, magic, and coherence. These resources can reach their theoretical lower bounds, $\Omega(\log (t/\epsilon))$, which are also proven in this work. This implies that for fixed $t$ and $\epsilon$, entanglement, magic, and coherence do not scale with the system size, i.e., $O(1)$ with respect to the total number of qubits $n$. Moreover, we explicitly construct an ancilla-free shallow quantum circuit for generating such states by transforming $k$-qubit approximate state designs into $n$-qubit ones without increasing the support size. The depth of such a quantum circuit, $O(t [\log t]^3 \log n \log(1/\epsilon))$, is the most efficient among existing algorithms without ancilla qubits. A class of quantum circuits proposed in our work offers reduced cost for classical simulation of random quantum states, leading to potential applications in quantum information processing. As a concrete example, we propose classical shadow tomography using an estimator with superpositions between only two states, from which almost all quantum states can be efficiently certified by requiring only $O(1)$ measurements and classical post-processing time.

quant-ph↗

arXiv2025

Exciton photoemission from a ground state of a solid Ta2Pd3Te5

Excitons are bosonic quasiparticles with a variety of applications in optoelectronics, photosyn thesis, and dissipationless informatics, and their lifetime can become sufficiently long to form a quantum condensate. While exciton condensation has been predicted to occur as a ground state of a solid, so called an excitonic insulator, whose material realization has been elusive. Here we report the observation of direct photoemission signals from excitons in a ground state of a very recent excitonic insulator candidate Ta2Pd3Te5 below its metal-insulator transition temperature using orbital-selective angle-resolved photoemission spectroscopy. It is confirmed that the excitons have a lower energy than the valence band maximum to possibly drive the phase transition. This measurement further discloses the size and the unusual odd parity of the exciton wave function. The present finding opens an avenue toward applications of coherent excitons in solid systems and searching for exotic quantum phases of exciton condensates.

cond-mat.str-el↗

arXiv2025

Intertwined Orders in a Quantum-Entangled Metal

Entanglement underpins quantum information processing and computing, yet its experimental quantification in complex, many-body condensed matter systems remains a considerable challenge. Here, we reveal a highly entangled electronic phase proximate to a quantum metal-insulator transition, identified by resonant inelastic x-ray scattering interferometry. This approach reveals that entanglement across atomic sites generates characteristic interference patterns, which our model accurately reproduces, enabling extraction of a full entanglement spectrum and resolution of the underlying quantum states. Our analysis of the pyrochlore iridate Nd2Ir2O7 demonstrates that the system undergoes pronounced quantum fluctuations in its spin, orbital and charge degrees of freedom, even in the presence of a long-range 'all-in-all-out' antiferromagnetic order. Importantly, the observed entanglement signatures facilitate the coexistence of multiple exotic symmetry-breaking orders. Complementary investigations using Raman spectroscopy corroborate the presence of these hidden orders and their emergent excitations. In particular, we observe a two-magnon-bound state below the lowest single-magnon excitation energy, which, together with split phonon modes, provides strong evidence for cubic symmetry-breaking orders of magnetic origin juxtaposed with the all-in-all-out order. Our work thus establishes a direct link between quantum entanglement and emergent unconventional orders, opening new avenues for investigating quantum materials.

cond-mat.str-el↗

arXiv2025

$\mathbb{Z}_N$ generalizations of three-dimensional stabilizer codes

In this work, we generalize several three-dimensional Z2 stabilizer models--including the X-cube model, the three-dimensional toric code, and Haah's code--to their ZN counterparts. Under periodic boundary conditions, we analyze their ground state degeneracies and topological excitations, and uncover behaviors that strongly depend on system size. For the X-cube model, we identify excitations with mobility restricted under local operations but relaxed under nonlocal ones derived from global topology. These excitations, previously confined to open boundaries in the Z2 model, now appear even under periodic boundaries. In the toric code, we observe nontrivial braiding between string and point excitations despite the absence of ground state degeneracy, indicating long-range entanglement independent of topological degeneracy. Again, this effect extends from open to periodic boundaries in the generalized models. For Haah's code, we find new excitations--fracton tripoles and monopoles--that remain globally constrained, along with a relaxation of immobility giving rise to lineons and planons. These results reveal new forms of topological order and suggest a broader framework for understanding fracton phases beyond the conventional Z2 setting.

cond-mat.str-el↗

arXiv2025

Chiral Pseudogap Metal Emerging from a Disordered van der Waals Mott Insulator 1T-TaS2-xSex

The emergence of a pseudogap is a hallmark of anomalous electronic states formed through substantial manybody interaction but the mechanism of the pseudogap formation and its role in related emerging quantum states such as unconventional superconductivity remain largely elusive. Here, we report the emergence of an unusual pseudogap in a representative van der Waals chiral charge density wave (CDW) materials with strong electron correlation, 1T-TaS2, through isoelectronic substitute of S. We investigate systematically the evolution of electronic band dispersions of 1T-TaS2-xSex (0=<x=<2) using angle-resolved photoemission spectroscopy (ARPES). Our results show that the Se substitution induces a quantum transition from an insulating to a pseudogap metallic phase with the CDW order preserved. Moreover, the asymmetry of the pseudogap spectral function is found, which reflects the chiral nature of CDW structure. The present observation is contrasted with the previous suggestions of a Mott transition driven by band width control or charge transfer. Instead, we attribute the pseudogap phase to a disordered Mott insulator in line with the recent observation of substantial lateral electronic disorder. These findings provide a unique electronic system with chiral pseudogap, where the complex interplay between CDW, chirality, disorder, and electronic correlation may lead to unconventional emergent physics.

cond-mat.str-el↗