arXiv subjects

Guangyue Ji

Publications and source records attributed to Guangyue Ji.

14 recordsLinked to original sources

arXiv2026

Gossamer Superconductivity in Moiré WSe$_2$ Bilayer

Moiré transition metal dichalcogenides have served as a versatile platform for simulating Hubbard physics. Recent experiments have identified robust superconductivity in moiré bilayer WSe$_2$ for certain twist angles. Here, we propose the gossamer nature of the superconductivity recently discovered at half-filling and zero displacement field in twisted WSe$_2$. By mapping the moiré continuum system to an effective extended single-orbital Hubbard model on the triangular lattice, we employ renormalized mean-field theory to investigate the strong-coupling phase diagram. We find that a moderate Coulomb repulsion partially suppresses charge fluctuations while preserving a finite density of mobile doublons and holes. In this regime, the interplay between extended kinetic hoppings and antiferromagnetic superexchange stabilizes a chiral $d+id$ superconducting phase. Our results naturally account for the twist-angle-dependent evolution from a Mott insulator to a superconductor and eventually to a correlated metal. Furthermore, the model demonstrates that this half-filled pairing state vanishes rapidly upon density doping, consistent with experimental observations.

cond-mat.str-el↗

arXiv2026

Generalized Model Fractional Quantum Hall States on Lattices

Model wave functions are essential for studying fractional quantum Hall phases, yet lattice model states have so far been limited to bosonic systems with on-site interactions. In this work, by combining analytical and numerical methods, we systematically construct lattice model states for the Laughlin, Moore--Read, and general $\mathbb{Z}_k$ Read--Rezayi series. Our lattice-specific states are characterized by their idealized energy and entanglement features and are distinguished from their continuum counterparts by a modified clustering behavior. Our theory advances the understanding of the stability of topologically ordered phases and illustrates the organizing principles of the conformal Hilbert space on lattices. Practically, this work paves the way for further studying lattice-specific excitations and offers a constructive route for engineering topological orders within density interactions, with potential immediate implications for cold-atom and synthetic flat-band platforms.

cond-mat.str-el↗

arXiv2025

Dynamics of Anyon Clusters in Fractional Quantum Hall Fluids

In fractional quantum Hall fluids, the quasiparticle excitations are anyons with fractional charges and statistics. Effective interactions among the anyons can be induced by either model or realistic electron-electron (e-e) interactions. Without losing the generality, we investigate such phenomena for the Laughlin 1/3 and Moore-Read (MR) non-Abelian phases. Anyons display rich internal dynamics in both cases that will lead to interesting experimental consequences. In particular, bound states of two Laughlin anyons are preferred under short-range e-e interactions, leading to 2e/3 -- instead of e/3 -- effective charge carriers at low temperatures, which have been seen in several experiments. MR phases host two topologically distinct fusion channels: 1 and psi. The different effective interactions of e/4 anyons in the two sectors suggest the vanishing of the degeneracy of fusion channels when the e-e interaction is no longer its model Hamiltonian, in which case different bound states could also appear. This indicates the possibility of energetically manipulating the two types of anyons by tuning the bare e-e interactions. We point out that the results of recently developed high-resolution STM measurements will be affected by the effective anyon interactions, where anyons are clustered together after the tunneling of electrons. The low-lying parts of the local density of states affected by various anyon clusters are simulated for both Abelian and non-Abelian systems with (screened) Coulomb interactions.

cond-mat.str-el↗

arXiv2025

Robust translational invariance in topological bands against lattice potentials and disorders

We theoretically show that the continuous magnetic translational invariance within the Hilbert (sub-)space of a single Landau level (LL) can persist even in the presence of a superlattice electrostatic potential modulation, while such invariance is broken in the full real-space Hilbert space. This is due to the interplay of the superlattice constant and the fundamental length scale of the quantum Hall fluids. In particular for the lowest LL (LLL), when the spacing of superlattice is below the magnetic length, continuous magnetic translational symmetry is very robust. For the fractional quantum Hall phases, the continuous translational symmetry is preserved when the superlattice spacing is below the corresponding fundamental lengths which we can now quantitatively define, which is different from the length scale from the quantum metric. Moreover, our analysis implies that the dynamics of the anyonic excitations can be robust against the long wavelength part of the disorder, and we discuss the related experimental ramifications.

cond-mat.str-el↗

arXiv2025

Density Matrix Geometry and Sum Rules

Geometry plays a fundamental role in a wide range of physical responses, from anomalous transport coefficients to their related sum rules. Notable examples include the quantization of the Hall conductivity and the Souza-Wilkens-Martin (SWM) sum rule -- both valid at zero temperature, independent of interactions and disorder. The finite-temperature generalization of the SWM sum rule has been explored in the literature, revealing deep connections to the geometry of density matrices. Building on recent advances in time-dependent geometric frameworks, we propose a time-dependent quantum geometric tensor for thermal density matrices. This formalism provides a unified interpretation of known sum rules within the framework of the fluctuation-dissipation theorem, further elucidating their fundamental geometric origin. In addition, it provides experimentally accessible methods to probe quantum geometry beyond the zero-temperature regime.

cond-mat.mes-hall↗

arXiv2025

Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders

In this work, we revisit the operator-state correspondence in the Majorana conformal field theory (CFT) with emphasis on its semion representation. Whereas the semion representation (or $Z_{2}$ extension of the chiral Ising CFT) gives a concise ``abelian" (or invertible) representation in the level of fusion rule and quantum states, there exists subtlety when considering the chiral multipoint correlation function. In this sense, the operator-state correspondence in the semion sector of the fermionic theory inevitably contains difficulty coming from its anomalous conformal dimension $1/16$ as a $Z_{2}$ symmetry operator. By analyzing the asymptotic behaviors of the existing correlation functions, we propose a nontrivial correspondence between the chiral conformal blocks and bulk correlation functions containing both order and disorder fields. One can generalize this understanding to $Z_{N}$ models or fractional supersymmetric models (in which there exist long-standing open problems). We expect this may improve our understanding of the simple current extension of CFT which can appear commonly in the studies of topologically ordered systems.

hep-th↗

arXiv2025

Dynamics and lifetime of geometric excitations in moiré systems

We show that spin-2 geometric excitations, known as graviton modes, generally exhibit vanishing lifetimes in lattice Chern bands, including in moiré systems. In contrast to the Landau levels, we first numerically demonstrate that the prominent graviton peaks in spectral functions diminish rapidly with increasing system sizes. We explore how the choice of interaction affects the strength of these peaks, with short-ranged interactions pushing the graviton mode far into the continuum of excitations, where it can be significantly scattered due to the increased density of states. We also analytically investigate the short lifetime of the graviton mode. In lattice systems, continuous rotational symmetry is broken, leading to highly anisotropic gapped excitations that mix different angular momentum or ``spins''. This is despite the surprising emergence of a ``guiding center" continuous rotational symmetry in the ground state, which is shared by the graviton mode. Consequently, the graviton mode in Chern bands can be strongly scattered by the anisotropic gapped excitations. However, the emergent rotational symmetry implies that gravitons can be robust in principle, and we propose experimental tuning strategies to lower the graviton mode energy below the continuum. We argue this is a necessary condition enabling the observation of graviton modes and geometric excitations in realistic moiré systems.

cond-mat.str-el↗

arXiv2025

Exact Parent Hamiltonians for All Landau Level States in a Half-flux Lattice

Realizing topological flat bands with tailored single-particle Hilbert spaces is a critical step toward exploring many-body phases, such as those featuring anyonic excitations. One prominent example is the Kapit-Mueller model, a variant of the Harper-Hofstadter model that stabilizes lattice analogs of the lowest Landau level states. The Kapit-Mueller model is constructed based on the Poisson summation rule, an exact lattice sum rule for coherent states. In this work, we consider higher Landau-level generalizations of the Poisson summation rule, from which we derive families of parent Hamiltonians on a half-flux lattice which have exact flat bands whose flatband wavefunctions are lattice version of higher Landau level states. Focusing on generic Bravais lattices with only translation and inversion symmetries, we discuss how these symmetries enforced gaplessness and singular points for odd Landau level series, and how to achieve fully gapped parent Hamiltonians by mixing even and odd series. Our model points to a large class of tight-binding models with suitable energetic and quantum geometries that are potentially useful for realizing non-Abelian fractionalized states when interactions are included. The model exhibits fast decay hopping amplitudes, making it potentially realizable with neutral atoms in optical lattices.

cond-mat.mes-hall↗

arXiv2024

Quantum metric induced hole dispersion and emergent particle-hole symmetry in topological flat bands

The emergent hole dispersion in flat bands is an invaluable platform to study the interplay of quantum geometry and electron-electron interaction with a relatively simple setting. In this work, we find that the hole dispersion in ideal bands has a linear relationship with the trace of the quantum geometry tensor at every $\boldsymbol{k}$-point for a wide range of interactions to a good approximation. Next, we give a microscopic analysis on the hole dispersion and show that the linear relationships for short-range and long-range interactions in $\boldsymbol{k}$-space have different origins. Moreover, we show how to exploit this observation to engineer particle-hole symmetry in a Chern band with fluctuating quantum geometry. Our results will be useful for further studying the physics in particle-hole symmetric flat bands both in theory and in experiment.

cond-mat.str-el↗

arXiv2024

Universal Modelling of Oscillations in Fractional Quantum Hall Fluids

Density oscillations in quantum fluids can reveal their fundamental characteristic features. In this work, we study the density oscillation of incompressible fractional quantum Hall (FQH) fluids created by flux insertion. For the model Laughlin state, we find that the complex oscillations seen in various density profiles in real space can be universally captured by a simple damped oscillator model in the occupation-number space. It requires only two independent fitting parameters or characteristic length scales: the decay length and the oscillation wave number. Realistic Coulomb quasiholes can be viewed as Laughlin quasiholes dressed by magnetorotons, which can be modeled by a generalized damped oscillator model. Our work reveals the fundamental connections between the oscillations seen in various aspects of FQH fluids such as in the density of quasiholes, edge, and the pair correlation function. The presented model is useful for the study of quasihole sizes for their control and braiding in experiments and large-scale numerical computation of variational energies.

cond-mat.str-el↗

arXiv2022

Quantum anomalous Hall insulator of composite fermions in twisted bilayer graphene

Abstract We theoretically study the realization of quantum anomalous Hall insulator (QAHI) of composite fermions (CFs) in the twisted bilayer graphene (TBG) system. We show that the moiré pattern in TBG is not only able to provide a commensurate moiré superlattice, but also a tunable effective periodic potential necessary for the realization, without the need of imposing an additional superstructure as in the conventional GaAs system. These make the TBG an ideal platform for realizing the QAHI of CFs. We establish the phase diagram with respect to tunable experimental parameters based on the Dirac CF theory. We find that the topological property of the system depends critically on the orbital magnetic susceptibility of CFs, which is not specified in the pristine Dirac CF theory. The experimental realization of QAHI of CFs would be helpful for unveiling the magnetic property of CFs and clarifying the issue.

cond-mat.mes-hall↗

arXiv2021

Emergence of Dirac Composite Fermions: Dipole Picture

Composite fermions (CFs) are the particles underlying the novel phenomena observed in partially filled Landau levels. Both microscopic wave functions and semi-classical dynamics suggest that a CF is a dipole consisting of an electron and a double $2h/e$ quantum vortex, and its motion is subject to a Berry curvature that is uniformly distributed in the momentum space. Based on the picture, we study the electromagnetic response of composite fermions. We find that the response in the long-wavelength limit has a form identical to that of the Dirac CF theory. To obtain the result, we show that the Berry curvature contributes a half-quantized Hall conductance which, notably, is independent of the filling factor of a Landau level and not altered by the presence of impurities. The latter is because CFs undergo no side-jumps when scattered by quenched impurities in a Landau-level with the particle-hole symmetry. The remainder of the response is from an effective system that has the same Fermi wavevector, effective density, Berry phase, and therefore long-wavelength response to electromagnetic fields as a Dirac CF system. By interpreting the half-quantized Hall conductance as a contribution from a redefined vacuum, we can explicitly show the emergence of a Dirac CF effective description from the dipole picture. We further determine corrections due to electric quadrupoles and magnetic moments of CFs and show deviations from the Dirac CF theory when moving away from the long wavelength limit.

cond-mat.mes-hall↗

arXiv2020

Berry phase of the composite Fermi-liquid

We derive the definition of the Berry phase for the adiabatic transport of a composite fermion (CF) in a half-filled composite Fermi-liquid (CFL). It is found to be different from that adopted in previous investigations by Geraedts et al. For the standard CFL wave function, we analytically show that the Berry curvature is uniformly distributed in the momentum space. For the Jain-Kamilla wave function, we numerically show that its Berry curvature has a continuous distribution inside the Fermi sea and vanishes outside. We conclude that the CF with respect to both the microscopic wave-functions is not a massless Dirac particle.

cond-mat.str-el↗

arXiv2020

Asymmetry of the Geometrical Resonances of Composite Fermions

We propose an experiment to test the uniform-Berry-curvature picture of composite fermions. We show that the asymmetry of geometrical resonances observed in a periodically modulated composite fermion system can be explained with the uniform-Berry-curvature picture. Moreover, we show that an alternative way of modulating the system, i.e., modulating the external magnetic field, will induce an asymmetry opposite to that of the usual periodic grating modulation which effectively modulates the Chern-Simons field. The experiment can serve as a critical test of the uniform-Berry-curvature picture, and probe the dipole structure of composite fermions proposed by Read.

cond-mat.mes-hall↗