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We show that spin-2 geometric excitations, known as graviton modes, generally exhibit vanishing lifetimes in lattice Chern bands, including in moir\'e 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 moir\'e systems., Comment: 9 pages, 4 figures, comments very welcome

We study fluctuation properties in the energy spectra of finite-size honeycomb lattices, graphene billiards, subject to the Haldane-model onsite potential and next-nearest neighbor interaction at critical points, referred to as Haldane graphene billiards in the following. The billiards had the shapes of a rectangular billiard with integrable dynamics, one with chaotic dynamics, and one whose shape has, in addition, threefold rotational symmetry. It had been shown that the spectral properties of the graphene billiards coincide with those of the nonrelativistic quantum billiard with the corresponding shape, both at the band edges and in the region of low energy excitations around the Dirac points at zero energy. There, the dispersion relation is linear and, accordingly, the spectrum is described by the same relativistic Dirac equation for massless half-spin particles as relativistic neutrino billiards, whose spectral properties agree with those of nonrelativistic quantum billiards with violated time-reversal invariance. Deviations from the expected behavior are attributed to differing boundary conditions and backscattering at the boundary, which leads to a mixing of valley states corresponding to the two Dirac points, that are mapped into each other through time reversal. We employ a Haldane model to introduce a gap at one of the two Dirac points so that backscattering is suppressed in the energy region of the gap and demonstrate that there the correlations in the spectra comply with those of the neutrino billiard of the corresponding shape.

3+1 dimensional topological phases can support loop-like excitations in addition to point-like ones, allowing for non-trivial loop-loop and point-loop braiding statistics not permitted to point-like excitations alone. Furthermore, these loop-like excitations can be linked together, changing their properties. In particular, this can lead to distinct three-loop braiding, involving two loops undergoing an exchange process while linked to a third loop. In this work, we investigate the loop-like excitations in a 3+1d Hamiltonian realization of Dijkgraaf-Witten theory through direct construction of their membrane operators, for a general finite Abelian group and 4-cocycle twist. Using these membrane operators, we find the braiding relations and fusion rules for the loop-like excitations, including those linked to another loop-like excitation. Furthermore, we use these membrane operators to construct projection operators that measure the topological charge and show that the number of distinct topological charges measured by the 2-torus matches the ground state degeneracy of the model on the 3-torus, explicitly confirming a general expectation for topological phases. This direct construction of the membrane operators sheds significant light on the key properties of the loop-like excitations in 3+1 dimensional topological phases., Comment: 35 pages + 29 pages supplemental material, 37 figures, v2: arXiv metadata corrected

Despite a long history of studies of vortex crystals in rotating superfluids, their melting due to quantum fluctuations is poorly understood. Here we develop a fracton-elasticity duality to investigate a two-dimensional vortex lattice within the fast rotation regime, where the Lifshitz model of the collective Tkachenko mode serves as the leading-order low-energy effective theory. We incorporate topological defects and discuss several quantum melting scenarios triggered by their proliferation. Furthermore, we lay the groundwork for a dual non-linear emergent gravity description of the superfluid vortex crystals., Comment: v2: SciPost submission

We examine the condensation and confinement mechanisms exhibited by a deformed toric code model proposed in [Castelnovo and Chamon, Phys. Rev. B, 2008]. The model describes both sides of a phase transition from a topological phase to a trivial phase. Our findings reveal an unconventional confinement mechanism that governs the behavior of the toric code excitations within the trivial phase. Specifically, the confined magnetic charge can still be displaced without any energy cost, albeit only via the application of non-unitary operators that reduce the norm of the state. This peculiar phenomenon can be attributed to a previously known feature of the model: it maintains the non-trivial ground state degeneracy of the toric code throughout the transition. We describe how this degeneracy arises in both phases in terms of spontaneous symmetry breaking of a generalized (1-form) symmetry and explain why such symmetry breaking is compatible with the trivial phase. The present study implies the existence of subtle considerations that must be addressed in the context of recently posited connections between topological phases and broken higher-form symmetries., Comment: 19 pages plus 13 pages of appendices, 8 figures, Submission to Scipost, v2: references added, typos fixed, added comments on 't Hooft anomalies, v3: new section about more general models

Half-integer quantized flux vortices appear in honeycomb lattices when the signs of an odd number of couplings around a plaquette are inverted. We show that states trapped at these vortices can be isolated by applying inhomogeneous strain to the system. A vortex then results in localized mid-gap states lying between the strain-induced pseudo-Landau levels, with $2n+1$ midgap states appearing between the $n$th and the $n+1$st level. These states are well-defined spectrally isolated and spatially localized excitations that could be realized in electronic and photonic systems based on graphene-like honeycomb lattices. In the context of Kitaev's honeycomb model of interacting spins, the mechanism improves the localization of non-Abelian anyons in the spin-liquid phase, and reduces their mutual interactions. The described states also serve as a testbed for fundamental physics in the emerging low-energy theory, as the correct energies and degeneracies of the excitations are only replicated if one accounts for the effective hyperbolic geometric induced by the strain. We further illuminate this by considering the effects of an additional external magnetic field, resulting in a characteristic spatial dependence that directly maps out the inhomogeneous metric of the emerging hyperbolic space., Comment: 17 pages with Appendix, 14 Figures. Comments are welcome!

We construct an effective field theory describing the collective Tkachenko oscillation mode of a vortex lattice in a two-dimensional rotating Bose-Einstein condensate in the long-wavelength regime. The theory has the form of a noncommutative field theory of a Nambu-Goldstone boson, which exhibits a noncommutative version of dipole symmetry. From the effective field theory, we show that, at zero temperature, the decay width $\Gamma$ of the Tkachenko mode scales with its energy $E$ as $\Gamma\sim E^3$ in the low-energy limit. We also discuss the width of the Tkachenko mode at a small temperature., Comment: 6+8 pages. Accepted version to Physical Review Research Letters!

Supersymmetry and supergravity were invented in the 1970s to solve fundamental problems in high-energy physics. Even though neither of these ideas has yet been confirmed in high-energy and cosmology experiments, they have been beneficial in constructing numerous theoretical models, including superstring theory. Despite the absence of supersymmetry in particle physics, it can potentially emerge in exotic phases of strongly correlated condensed matter systems. In this paper, we propose a supergravity model that describes the low-energy physics of the Haldane-Rezayi state, a gapless quantum Hall state that occurs in a half-filled Landau level. We show that the corresponding edge modes of the Haldane-Rezayi state and the Girvin-MacDonald-Platzman algebra appear naturally in the supergravity model. Finally, we substantiate our theoretical findings with numerical exact diagonalization calculations that support the appearance of the emergent graviton and gravitino excitations in the Haldane-Rezayi state., Comment: v2: new appendix B deriving the explicit action, updated references, matches published version. v1: 11 pages 1 figure. Comments are welcome

The interplay between symmetry and topology led to the discovery of symmetry-protected topological phases in Hermitian systems, including topological insulators and topological superconductors. However, the intrinsic symmetry-protected topological characteristics of non-Hermitian systems still await exploration. Here, we investigate experimentally the topological transition associated with the inversion of non-Hermitian band structures in an optical lattice. Intriguingly, we demonstrate that the winding number associated with the symmetry-protected bound state in the continuum is not a conserved quantity after band inversion. To define a topological invariant, we propose the skyrmion number given by spawning in momentum space a pseudo-spin with the polarisation vortex as the in-plane component and the band-index as the pseudo-spin direction at the origin. This leads to a topological transition from an antimeron to an meron-like texture through band inversion, while always conserving the half-charge skyrmion number. We foresee the use of skyrmion number to explore exotic singularities in various non-Hermitian physical system.

The chiral surface states of Weyl semimetals have an open Fermi surface called Fermi arc. At the interface between two Weyl semimetals, these Fermi arcs are predicted to hybridize and alter their connectivity. In this letter, we numerically study a one-dimensional (1D) dielectric trilayer grating where the relative displacements between adjacent layers play the role of two synthetic momenta. The lattice emulates 3D crystals without time-reversal symmetry, including Weyl semimetal, nodal line semimetal, and Chern insulator. Besides showing the phase transition between Weyl semimetal and Chern insulator at telecom wavelength, this system allows us to observe the Fermi arc reconstruction between two Weyl semimetals, confirming the theoretical predictions., Comment: Main text: 4 pages, 4 figures. Supplemental materials: 19 pages, 18 figures

We study numerically the the charge neutral excitations (magnetorotons) in fractional quantum Hall systems, concentrating on the two Jain states near quarter filling, $\nu=2/7$ and $\nu=2/9$, and the $\nu=1/4$ Fermi-liquid state itself. In contrast to the $\nu=1/3$ states and the Jain states near half filling, on each of the two Jain states $\nu=2/7$ and $\nu=2/9$ the graviton spectral densities show two, instead of one, magnetoroton peaks. The magnetorotons have spin 2 and have opposite chiralities in the $\nu=2/7$ state and the same chirality in the $\nu=2/9$ state. We also provide a numerical verification of a sum rule relating the guiding center spin $\bar s$ with the spectral densities of the stress tensor, Comment: 6+2 pages. 9 Figures. Comments are welcome!

We propose a programmable photonic platform that integrates Thouless pumping and reconfigurable lasing in sliding bilayer photonic crystals. By engineering two periodic potentials -- a slowly moving photonic grating atop a stationary one -- we demonstrate how their interplay yields distinct topological phases characterized by either robust light transport (Thouless pumping) or localized spatial oscillation (trapping). A heterojunction between crystals in these two regimes supports an interface mode stemming from the topological phase transition across the boundary. This interface mode can be actively tuned via microelectromechanical systems or switched through the integration of phase-change materials. We further establish the feasibility of lasing action at this interface mode, offering a pathway toward topologically robust and reconfigurable lasers. Our findings provide a framework for exploring topological phase transitions and unify the fields of topological photonics and programmable photonic devices, opening avenues for multidimensionally tunable light sources., Comment: New version with significant changes. Comments are welcome!

We reconsider the composite fermion theory of general Jain's sequences with filling factor $\nu=N/(4N\pm1)$. We show that Goldman and Fradkin's proposal of a Dirac composite fermion leads to a violation of the Haldane bound on the coefficient of the static structure factor. To resolve this apparent contradiction, we add to the effective theory a gapped chiral mode (or modes) which already exists in the Fermi liquid state at $\nu=1/4$. We interpret the additional mode as an internal degree of freedom of the composite fermion, related to area-preserving deformations of the elementary droplet built up from electrons and correlation holes. In addition to providing a suitable static structure factor, our model also gives the expected Wen-Zee shift and a Hall conductivity that manifests Galilean invariance. We show that the charge density in the model satisfies the long-wavelength version of the Girvin-MacDonald-Platzman algebra., Comment: Accepted version to Physical Review Research, added a derivation of Haldane bound using lowest Landau level Ward's identities,comments are welcome!

We investigate the physics of photonic band structures of the moir\'e patterns that emerged when overlapping two uni-dimensional (1D) photonic crystal slabs with mismatched periods. The band structure of our system is a result of the interplay between intra-layer and inter-layer coupling mechanisms, which can be fine-tuned via the distance separating the two layers. We derive an effective Hamiltonian that captures the essential physics of the system and reproduces all numerical simulations of electromagnetic solutions with high accuracy. Most interestingly, \textit{magic distances} corresponding to the emergence of photonic flatbands within the whole Brillouin zone of the moir\'e superlattice are observed. We demonstrate that these flatband modes are tightly localized within a moir\'e period. Moreover, we suggest a single-band tight-binding model that describes the moir\'e minibands, of which the tunnelling rate can be continuously tuned via the inter-layer strength. Our results show that the band structure of bilayer photonic moir\'e can be engineered in the same fashion as the electronic/excitonic counterparts. It would pave the way to study many-body physics at photonic moir\'e flatbands and novel optoelectronic devices., Comment: 6 pages + Supplement. Comments are welcome!

We propose nonabelian higher-rank gauge theories in 2+1D and 3+1D. The gauge group is constructed from the volume-preserving diffeomorphisms of space. We show that the intriguing physics of the lowest Landau level (LLL) limit can be interpreted as the consequences of the symmetry. We derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term within our formalism. Using the gauge symmetry in 2+1D, we derive the LLL effective action of vortex crystal in rotating Bose gas as well as Wigner crystal of electron in an applied magnetic field. We show that the nonlinear sigma models of ferromagnets in 2+1D and 3+1D exhibit the higher-rank gauge symmetries that we introduce in this paper. We interpret the fractonic behavior of the excitations on the lowest Landau level and of skyrmions in ferromagnets as the consequence of the higher-rank gauge symmetry., Comment: Typos are fixed. Comments are welcome!

Starting from the Luttinger model for the band structure of GaAs, we derive an effective theory that describes the coupling of the fractional quantum Hall (FQH) system with photons in resonant Raman scattering experiments. Our theory is applicable in the regime when the energy of the photons $\omega_0$ is close to the energy gap $E_G$, but $|\omega_0-E_G|$ is much larger than the energy scales of the quantum Hall problem. In the literature, it is often assumed that Raman scattering measures the dynamic structure factor $S(\omega,\mathbf{k})$ of the FQH. However, in this paper, we find that the light scattering spectrum measured in the experiments are proportional to the spectral densities of a pair of operators which we identified with the spin-2 components of the kinetic part of the stress tensor. In contrast with the dynamic structure factor, these spectral densities do not vanish in the long-wavelength limit $k\to0$. We show that Raman scattering with circularly polarized light can measure the spin of the magnetoroton excitation in the FQH system. We give an explicit expression for the kinetic stress tensor that works on any Landau level and which can be used for numerical calculations of the spectral densities that enter the Raman scattering amplitudes. We propose that Raman scattering provides a way to probe the bulk of the $\nu=5/2$ quantum Hall state to determine its nature., Comment: 25 pages, 1 figure. Comments are welcome!

We construct a minimal theory describing the optical activity of a thin sheet of a twisted material, the simplest example of which is twisted bilayer graphene. We introduce the notion of "twisted electrical conductivity", which parametrizes the parity-odd response of a thin film to a perpendicularly falling electromagnetic waves with wavelength larger than the thickness of the sheet. We show that the low-frequency Faraday rotation angle has different behaviors in different phases. For an insulator, the Faraday angle behaves as $\omega^2$ at low frequencies, with the coefficient being determined by the linear relationship between a component of the electric quadrupole moment and the external electric field. For superconductors, the Faraday rotation angle is constant when the frequency of the incoming EM waves is below the superconducting gap and is determined by the coefficient of the Lifshitz invariant in the Ginzburg-Landau functional describing the superconducting state. In the metallic state, we show that the twisted conductivity is proportional to the "magnetic helicity" (scalar product of the velocity and the magnetic moment) of the quasiparticle, averaged around the Fermi surface. The theory is general and is applicable to strongly correlated phases., Comment: 6+7 pages. Comments are welcome

Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex supersolid phase., Comment: Scipost Physics accepted version

We construct an algebraic description for the ground state and for the static response of the quantum Hall plateaux with filling factor $\nu=N/(2N+1)$ in the large $N$ limit. By analyzing the algebra of the fluctuations of the shape of the Fermi surface of the composite fermions, we find the explicit form of the projected static structure factor at large $N$ and fixed $z=(2N+1) q\ell_B\sim 1$. When $z<3.8$, the result does not depend on the particular form of the Hamiltonian., Comment: 5 pages, 1 figure

We perform a detailed comparison of the Dirac composite fermion and the recently proposed bimetric theory for a quantum Hall Jain states near half filling. By tuning the composite Fermi liquid to the vicinity of a nematic phase transition, we find that the two theories are equivalent to each other. We verify that the single mode approximation for the response functions and the static structure factor becomes reliable near the phase transition. We show that the dispersion relation of the nematic mode near the phase transition can be obtained from the Dirac brackets between the components of the nematic order parameter. The dispersion is quadratic at low momenta and has a magnetoroton minimum at a finite momentum, which is not related to any nearby inhomogeneous phase., Comment: 13 pages, 1 figure

We study fractional quantum Hall states at filling fractions in the Jain sequences using the framework of composite Dirac fermions. Synthesizing previous work, we write down an effective field theory consistent with all symmetry requirements, including Galilean invariance and particle-hole symmetry. Employing a Fermi liquid description, we demonstrate the appearance of the Girvin--Macdonlald--Platzman algebra and compute the dispersion relation of neutral excitations and various response functions. Our results satisfy requirements of particle-hole symmetry. We show that while the dispersion relation obtained from the HLR theory is particle-hole symmetric, correlation functions obtained from HLR are not. The results of the Dirac theory are shown to be consistent with the Haldane bound on the projected structure factor, while those of the HLR theory violate it., Comment: 32 pages, 3 figures

We derive a number of exact relations between response functions of holomorphic, chiral fractional quantum Hall states and their particle-hole (PH) conjugates. These exact relations allow one to calculate the Hall conductivity, Hall viscosity, various Berry phases, and the static structure factor of PH-conjugate states from the corresponding properties of the original states. These relations establish a precise duality between chiral quantum Hall states and their PH-conjugates. The key ingredient in the proof of the relations is a generalization of Girvin's construction of PH-conjugate states to inhomogeneous magnetic field and curvature. Finally, we make several non-trivial checks of the relations, including for the Jain states and their PH-conjugates., Comment: 10 pages

We present a simple method that allows to calculate the electromagnetic response of non-interacting electrons in strong magnetic field to arbitrary order in the gradients of external electric and magnetic fields. We illustrate the method on both non-relativistic and massless Dirac electrons filling $N$ Landau levels. First, we derive an exact relation between the electromagnetic response of the non-relativistic and Dirac electrons in the lowest Landau level. Next, we obtain a closed form expression for the polarization operator in the large $N$ (or weak magnetic field) limit. We explicitly show that in the large $N$ limit the random phase approximation (RPA) computation of the polarization tensor agrees - in leading and sub-leading order in $N$ - with a Fermi liquid computation to {\it all} orders in the gradient expansion and for arbitrary value of the $\mathrm{g}$-factor. Finally, we show that in the large $N$ limit the non-relativistic polarization tensor agrees with Dirac's in the leading and sub-leading orders in $N$, provided that Berry phase of the Dirac cone is taken into account via replacement $N\longrightarrow N+\frac{1}{2}$., Comment: 23 pages, 5 figures

Fractional quantum Hall liquids exhibit a rich set of excitations, the lowest-energy of which are the magnetorotons with dispersion minima at a finite momentum. We propose a theory of the magnetorotons on the quantum Hall plateaux near half filling, namely, at filling fractions $\nu=N/(2N+1)$ at large $N$. The theory involves an infinite number of bosonic fields arising from bosonizing the fluctuations of the shape of the composite Fermi surface. At zero momentum there are $O(N)$ neutral excitations, each carrying a well-defined spin that runs integer values $2,3,\ldots$. The mixing of modes at nonzero momentum $q$ leads to the characteristic bending down of the lowest excitation and the appearance of the magnetoroton minima. A purely algebraic argument shows that the magnetoroton minima are located at $q\ell_B=z_i/(2N+1)$, where $\ell_B$ is the magnetic length and $z_i$ are the zeros of the Bessel function $J_1$, independent of the microscopic details. We argue that these minima are universal features of any two-dimensional Fermi surface coupled to a gauge field in a small background magnetic field., Comment: 5 pages, 2 figures; v3: published version

We show that for a class of model Hamiltonians for which certain trial quantum Hall wavefunctions are exact ground states, there is a single spectral density function which controls all two-point correlation functions of density, current and stress tensor components. From this we show that the static structure factors of these wavefunctions behaves at long wavelengths as $s_4 k^4$ where the coefficient $s_4$ is directly related to the shift: $s_4=(\mathcal S-1)/8$., Comment: 5 pages