Although individual skyrmions are topologically protected objects, their cooperative crystalline order is fragile, easily disrupted by thermal fluctuations or other external perturbations. Probing the internal dynamics of such a crystal is both compelling and challenging, as its intricate and delicate spin texture must remain stable during measurement. Here, we engineer a nanoscale graphene junction hosting a skyrmion Wigner crystal, embedded between magnon emitters and detectors. The skyrmion crystal geometry leaves a striking imprint on magnon transport: as the gate voltage is varied, near-periodic windows of sharp fluctuations in magnon count are detected across the entire sample. We develop an interpretation that this results from skyrmions being added one by one to a quasi-one-dimensional array. Each burst of the fluctuations thus corresponds to the entry of an additional skyrmion, during which the lattice stiffness reduces. The impinging magnons induce and act as a probe of non-equilibrium collective dynamics of the crystal. These results establish a real-space probe of topological spin textures in quantum Hall-type insulating ground states via magnon transport and open opportunities to explore correlated, topologically ordered phases in moire and multilayer graphene systems.

We compute the degeneracy of energy levels in the Kitaev quantum double model for any discrete group G on any planar graph forming the skeleton of a closed orientable surface of arbitrary genus. The derivation is based on the fusion rules of the properly identified vertex and plaquette excitations, which are selected among the anyons, i.e., the simple objects of the Drinfeld center Z(VecG). These degeneracies are given in terms of the quantum dimensions of the anyons and allow one to obtain the exact finite-temperature partition function of the model, valid for any finite-size system.

We study conventional and out-of-time-ordered correlators (OTOCs) for a wide variety of transverse field Ising chains: classical and quantum, clean and disordered, and integrable and generic. The setting we consider is that of a quantum quench. We find a remarkably rich phenomenology, ranging from stable periodic signals to ones decaying with varying rates. This variety is due to a complex interplay of constraints on thermalization imposed by integrability and symmetry. A process we term dynamical domain wall relocalization provides a long-lived signal in the clean, integrable case, which can be degraded by the addition of disorder even without interactions. Our results shed light on a proposal to use an OTOC as a dynamical diagnostic of a quantum phase more powerful than a standard observable.

A crucial ingredient for scalable, fault-tolerant quantum computing is the construction of logical qubits with low error rates and intrinsic noise protection. We propose a cross-platform construction for such hardware-level noise protection, in which the qubits are protected from depolarizing (relaxation) and dephasing errors induced by local noise. These logical qubits arise from the entanglement between two internal degrees of freedom, hence we term them entanglemons. Our construction is based on the emergence of collective degrees of freedom from a generalized coherent state construction, similar in spirit to spin coherent states, of a set of such internally entangled units. These degrees of freedom, for a finite number of units, parametrize the quantized version of complex projective space CP(3). The noise protection of the entanglemon qubit is then a consequence of a weakly coupled emergent degree of freedom arising due to the nonlinear geometry of complex projective space. We present two simple models for entanglemons, which are platform agnostic, provide varying levels of protection, and in which the qubit-basis states are the two lowest-energy states with a higher-energy gap to other states. We end by commenting on how entanglemons could be realized in platforms ranging from superconducting circuits, and trapped ion platforms, to possibly also quantum Hall skyrmions in graphene and quantum dots in semiconductors. The inherent noise protection in our models combined with the platform agnosticism highlights the potential of encoding information in additional weakly coupled emergent degrees of freedom arising in nonlinear geometrical spaces and curved phase spaces, thereby proposing a different route to achieve scalable fault tolerance.

We present an analysis of the orbital Hall effect (OHE) in a strip geometry and derive a formula for the orbital angular momentum (OAM) accumulation at the edges. The result is expressed in terms of band structure parameters and scattering rates, providing a link between experimental observations of the OHE and the underlying microscopics. A key result is that the effective OAM decay rate follows a Dykonov-Perel-like scaling and is inversely proportional to the electron scattering rate, even if the latter is small. Furthermore, investigating OAM transport in an inhomogeneous setting, we show that non-Ohmic flows and spatially varying electric fields result in contributions to the OHE which are distinct from the well known intrinsic and extrinsic mechanisms.

Spontaneous symmetry breaking and more recently entanglement are two cornerstones of quantum matter. We introduce the notion of anisotropic entanglement ordered phases, where the spatial profile of spin-pseudospin entanglement spontaneously lowers the fourfold rotational symmetry of the underlying crystal to a twofold one, while the charge density retains the full symmetry. The resulting phases, which we term entanglement smectic and entanglement stripe, exhibit a rich Goldstone mode spectrum and a set of phase transitions as a function of underlying anisotropies. We discuss experimental consequences of such anisotropic entanglement phases distinguishing them from more conventional charge or spin stripes. Our discussion of this interplay between entanglement and spontaneous symmetry breaking focuses on multicomponent quantum Hall systems realizing textured Wigner crystals, as may occur in graphene or possibly also in moiré systems, highlighting the rich landscape and properties of possible entanglement ordered phases.

We consider a quantum topological frequency converter, realized by coupling a qubit to two slow harmonic modes. The dynamics of such a system is the quantum analog of topological pumping. Our quantum mechanical description shows that an initial state generically evolves into a superposition of two adiabatic states. The topological nature of the coupling between the qubit and the modes splits these two components apart in energy: for each component, an energy transfer at a quantized rate occurs between the two quantum modes, in opposite directions for the two components, reminiscent of the topological pumping. We denote such a superposition of two quantum adiabatic states distinguishable through measures of the modes' energy an adiabatic cat state. We show that the topological coupling enhances the entanglement between the qubit and the modes, and we unveil the role of the quantum or Fubini-Study metric in the characterization of this entanglement.

The discovery of the quantum Hall effect has established the foundation of the field of topological condensed matter physics. An amazingly accurate quantization of the Hall conductance, now enshrined in quantum metrology, is stable against any reasonable perturbation due to its topological protection. Conversely, the latter implies a form of censorship by concealing any local information from the observer. The spatial distribution of the current in a quantum Hall system is such a piece of information, which, thanks to spectacular recent advances, has now become accessible to experimental probes. It is an old question whether the original and intuitively compelling theoretical picture of the current, flowing in a narrow channel along the sample edge, is the physically correct one. Motivated by recent experiments locally imaging quantized current in a Chern insulator (Bi, Sb) 2 Te 3 heterostructure [Rosen et al., Phys. Rev. Lett. 129 , 246602 (2022); Ferguson et al., Nat. Mater. 22 , 1100–1105 (2023)], we theoretically demonstrate the possibility of a broad “edge state” generically meandering away from the sample boundary deep into the bulk. Further, we show that by varying experimental parameters one can continuously tune between the regimes with narrow edge states and meandering channels, all the way to the charge transport occurring primarily within the bulk. This accounts for various features observed in, and differing between, experiments. Overall, our findings underscore the robustness of topological condensed matter physics, but also unveil the phenomenological richness, hidden until recently by the topological censorship—most of which, we believe, remains to be discovered.

Semi-holography, originally proposed as a model for conducting lattice electrons coupled to a holographic critical sector, leads to an effective theory of non-Fermi liquids with only a few relevant interactions on the Fermi surface in the large $N$ limit. A refined version of such theories has only two effective couplings which give holographic and Fermi-liquid-like contributions to the self-energy, respectively. We show that a low co-dimension sub-manifold exists in the space of refined semi-holographic theories in which strange metallic behavior is manifested, and which can be obtained just by tuning the ratio of the two couplings. On this sub-manifold, the product of the spectral function and the temperature is approximately independent of the critical exponent, the Fermi energy, and the temperature at all frequencies and near the Fermi surface when expressed in terms of suitably scaled momentum and frequency variables. This quasi-universal behavior leads to linear-in-$T$ dc resistivity and Planckian dissipation over a large range of temperatures, and we also obtain $T^{-3}$ scaling of the Hall conductivity at higher temperatures. The quasi-universal spectral function also fits well with photoemission spectroscopic data without varying the critical exponent with the doping. Combining with the results for optical conductivity, we construct a generalized version of Drude phenomenology for strange-metallic behavior which satisfies non-trivial consistency tests. Finally, we discuss a possible dynamical mechanism for the fine-tuning of the ratio of the two couplings necessary to realize the strange metallic behavior in a typical state.

The exploration of atomic fractional quantum Hall (FQH) states is now within reach in optical-lattice experiments. While ground-state signatures have been observed in a system realizing the Hofstadter-Bose-Hubbard model in a box [Leonard et al., Nature 2023], how to access hallmark low-energy collective modes remains a central open question in this context. We introduce a spectroscopic scheme based on two interfering Laguerre-Gaussian beams, which transfer a controlled angular momentum and energy to the system. The edge and bulk responses to the probe are detected through local density measurements, by tracking the transfer of atoms between the bulk and the edge of the FQH droplet. This detection scheme is shown to simultaneously reveal two specific signatures of FQH states: their chiral edge branch and their bulk magneto-roton mode. We numerically benchmark our method by considering few bosons in the $\nu=1/2$ Laughlin ground state of the Hofstadter-Bose-Hubbard model, and demonstrate that these signatures are already detectable in realistic systems of two bosons, provided that the box potential is larger than the droplet. Our work paves the way for the detection of fractional statistics in cold atoms through edge signatures.

We study the three terminal S-QD-S-QD-S Josephson junction biased with commensurate voltages. In the absence of an applied voltage, the Andreev bound states on each quantum dot hybridize forming an `Andreev molecule'. However, understanding of this system in a non-equilibrium setup is lacking. Applying a dc voltage on the bijunction makes the system time-periodic, and the equilibrium Andreev bound states evolve into a ladder of resonances with a finite lifetime due to multiple Andreev reflections (MAR). Starting from the time-periodic Bogoliubov-de Gennes equations we map the problem to a tight-binding chain in the (infinite) Floquet space. The resolvent of this non-Hermitian block matrix is obtained via a continued fraction method. We numerically calculate the Floquet-Andreev spectra which could be probed by local tunneling spectroscopy on the dots. We also consider the subgap current, and show that the Floquet resonances determine the position of the MAR steps. Proximity of the two dots causes splitting of the steps, while at large distances we observe interference effects which cause oscillations in the I-V curves. The latter effect should persist at very long distances.

We introduce a model to study magnon scattering in skyrmion crystals, sandwiched between ferromagnets which act as the source of magnons. Skyrmions are topological objects while skyrmion crystals break internal and translational symmetries, thus our setup allows us to study the interplay of topology and symmetry breaking. Starting from a basis of holomorphic theta functions, we construct an analytical ansatz for such a junction with finite spatially modulating topological charge density in the central region and vanishing in the leads. We then construct a suitably defined energy functional for the junction and derive the resulting equations of motion, which resemble a Bogoliubov-de Gennes-like equation. Using analytical techniques, field theory, heuristic models and microscopic recursive transfer-matrix numerics, we calculate the spectra and magnon transmission properties of the skyrmion crystal. We find that magnon transmission can be understood via a combination of low-energy Goldstone modes and effective emergent Landau levels at higher energies. The former manifests in discrete low-energy peaks in the transmission spectrum which reflect the nature of the Goldstone modes arising from symmetry breaking. The latter, which reflect the topology, lead to band-like transmission features, from the structure of which further details of the excitation spectrum of the skyrmion crystal can be inferred. Such characteristic transmission features are absent in competing phases of the quantum Hall phase diagram, and hence provide direct signatures of skyrmion crystal phases and their spectra. Our results directly apply to quantum Hall heterojunction experiments in monolayer graphene with the central region doped slightly away from unit filling, a $\nu = 1:1 \pm \delta \nu: 1$ junction and are also relevant to junctions formed by metallic magnets or in junctions with artificial gauge fields.

We consider a Josephson bijunction consisting of three superconducting reservoirs connected through two quantum dots. In equilibrium, the interdot coupling is sizable only for distances smaller than the superconducting coherence length. Application of commensurate dc voltages results in a time-periodic Hamiltonian and induces an interdot coupling at large distances. The basic mechanism of this long-range coupling is shown to be due to local multiple Andreev reflections on each dot, followed by quasiparticle propagation at energies larger than the superconducting gap. At large interdot distances we derive an effective non-Hermitian Hamiltonian describing two resonances coupled through a continuum.

A refined semi-holographic non-Fermi liquid model, in which carrier electrons hybridize with operators of a holographic critical sector, has been proposed recently for strange metallic behavior. The model, consistently with effective theory approach, has two couplings whose ratio is related to the doping. We explain the origin of the linear-in-T resistivity and strange metallic behavior as a consequence of the emergence of a universal form of the spectral function which is independent of the model parameters when the ratio of the two couplings take optimal values determined only by the critical exponent. This universal form fits well with photoemission data of copper oxide samples for under/optimal/over-doping with a fixed exponent over a wide range of temperatures. We further obtain a refined Planckian dissipation scenario in which the scattering time $\tau = f \cdot \hbar /(k_B T)$, with $f$ being $\mathcal{O}(1)$ at strong coupling, but $\mathcal{O}(10)$ at weak coupling.

We construct a semi-holographic effective theory in which the electron of a two-dimensional band hybridizes with a fermionic operator of a critical holographic sector, while also interacting with other bands that preserve quasiparticle characteristics. Besides the scaling dimension ν of the fermionic operator in the holographic sector, the effective theory has two dimensionless couplings α and γ determining the holographic and Fermi-liquid-type contributions to the self-energy respectively. When ∼ 0.67 < ν <∼ 0.8, the DC resistivity is linear in T to a remarkably good approximation in a narrow range of α/γ and over a range of temperatures extending from about 0.3EF to about 20 − 40EF for small couplings. For higher values of ν lesser than unity which realizes a marginal Fermi liquid with a specific temperature dependence of the self-energy, we also find linear-in-T resistivity to reasonably good approximation in an even wider range of temperatures that extends to arbitrarily small values.

In this paper, we consider a quantum dot connected to four superconducting terminals biased at opposite voltages on the quartet line. The grounded superconductor contains a loop threaded by the magnetic flux Phi. We provide Keldysh microscopic calculations and physical pictures for the voltage-V dependence of the quartet current. Superconductivity is expected to be stronger at Phi/Phi(0) = 0 than at Phi/Phi(0) = 1/2. However, inversion I-q,I-c(V, 0) < I-q,I-c(V, 1/2) is obtained in the critical current I-q,I-c(V, Phi/Phi(0)) on the quartet line in the voltage-V ranges which match avoided crossings in the Floquet spectrum at (V, Phi/Phi(0) = 0) but not at (V, 1/2). A reduction in I-q,I-c appears in the vicinity of those avoided crossings, where Landau-Zener tunneling produces dynamical quantum mechanical superpositions of the Andreev bound states. In addition, pi-0 and 0-pi crossovers emerge in the current-phase relations as V is further increased. The voltage-induced pi shift is interpreted as originating from the nonequilibrium Floquet populations produced by voltage biasing. The numerical calculations reveal that the inversion is robust against strong Landau-Zener tunneling and many levels in the quantum dot. Our theory provides a simple "Floquet level and population" mechanism for inversion tuned by the bias voltage V, which paves the way towards more realistic models for the recent Harvard group experiment where the inversion is observed.

We study the neutral excitations of fractional quantum Hall states in electronic systems of finite width where an external anisotropy is introduced by tilting the magnetic field. As in the isotropic case, the neutral collective excitation can be worked out through the conserving method of composite fermions in the Hamiltonian theory because the interaction potential has a natural cutoff due to the quantum well width. We show how such a computation can be carried out perturbatively for an anisotropic interaction. We find that unlike the charge gap, the neutral collective gap is much more sensitive to the tilt and can thus, for certain fractional quantum Hall states, be easily destroyed by the parallel component of the magnetic field. We also discuss the convergence of the collective spectrum to the activation gap in the large-momentum limit.

We report on a study of the nontrivial Berry phase in superconducting multiterminal quantum dots biased at commensurate voltages. Starting with the time-periodic Bogoliubov--de Gennes equations, we obtain a tight-binding model in Floquet space, and we solve these equations in the semiclassical limit. We observe that the parameter space defined by the contact transparencies and quartet phase splits into two components with a nontrivial Berry phase. We use the Bohr-Sommerfeld quantization to calculate the Berry phase. We find that if the quantum dot level sits at zero energy, then the Berry phase takes the values ${\ensuremath{\varphi}}_{B}=0$ or ${\ensuremath{\varphi}}_{B}=\ensuremath{\pi}$. We demonstrate that this nontrivial Berry phase can be observed by tunneling spectroscopy in the Floquet spectra. Consequently, the Floquet-Wannier-Stark ladder spectra of superconducting multiterminal quantum dots are shifted by half-a-period if ${\ensuremath{\varphi}}_{B}=\ensuremath{\pi}$. Our numerical calculations based on the Keldysh Green's functions show that this Berry phase spectral shift can be observed from the quantum dot tunneling density of states.

Here we present a theoretical investigation of the Floquet spectrum in multiterminal quantum dot Josephson junctions biased with commensurate voltages. We first draw an analogy between the electronic band theory and superconductivity which enlightens the time-periodic dynamics of the Andreev bound states. We then show that the equivalent of the Wannier-Stark ladders observed in semiconducting superlattices via photocurrent measurements, appears as specific peaks in the finite frequency current fluctuations of superconducting multiterminal quantum dots. In order to probe the Floquet-Wannier-Stark ladder spectra, we have developed an analytical model relying on the sharpness of the resonances. The charge-charge correlation function is obtained as a factorized form of the Floquet wave function on the dot and the superconducting reservoir populations. We confirm these findings by Keldysh Green's function calculations, in particular regarding the voltage and frequency dependence of the resonance peaks in the current-current correlations. Our results open up a road map to quantum correlations and coherence in the Floquet dynamics of superconducting devices.

We use the Hamiltonian theory developed by Shankar and Murthy to study a quantum Hall system in a tilted magnetic field. With a finite width of the system in the $z$ direction, the parallel component of the magnetic field introduces anisotropy into the effective two-dimensional interactions. The effects of such anisotropy can be effectively captured by the recently proposed generalized pseudopotentials. We find that the off-diagonal components of the pseudopotentials lead to mixing of composite fermions Landau levels, which is a perturbation to the picture of $p$ filled Landau levels in composite-fermion theory. By changing the internal geometry of the composite fermions, such a perturbation can be minimized and one can find the corresponding activation gaps for different tilting angles, and we calculate the associated optimal metric. Our results show that the activation gap is remarkably robust against the in-plane magnetic field in the lowest and first Landau levels.