The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. Here, we construct a different type of fractional quantum Hall system, which has the special property that it lives in fractal dimensions. We provide analytical wave functions and exact few-body parent Hamiltonians, and we show numerically for several different Hausdorff dimensions between 1 and 2 that the systems host anyons. We also find examples of fractional quantum Hall physics in fractals with Hausdorff dimension 1 and $ln\left(4\right)/ln\left(5\right)$. Our results suggest that the local structure of the investigated fractals is more important than the Hausdorff dimension to determine whether the systems are in the desired topological phase. The study paves the way for further investigations of strongly correlated topological systems in fractal dimensions.

We present a phenomenological Green's function to characterize the superconducting and pseudogap phases of the cuprates based on a microscopic theory of doped Mott insulators. In this framework, the “Fermi-arc” and “kink” phenomena observed by angle-resolved photoemission spectroscopy experiments in the pseudogap phase can be systematically explained as a function of doping, which are further connected to the two-gap feature in the superconducting phase with dichotomy between the nodal and antinodal physics. We demonstrate that a phase-string-induced fractionalization plays the key role in giving rise to such a peculiar Green's function with a unique two-component structure.

Mössbauer nuclei feature exceptionally narrow resonances at hard x-ray energies, which render them ideal probes for structure and dynamics in condensed-matter systems, and a promising platform for x-ray quantum optics and fundamental tests. However, a direct spectroscopy at modern x-ray sources such as synchrotrons or x-ray free-electron lasers is challenging, because of the broad spectral bandwidth of the delivered x-ray pulses, and because of a limited spectral resolution offered by x-ray optics and detectors. To overcome these challenges, here, we propose a spectroscopy technique based on a spectrally narrow reference absorber that is rapidly oscillating along the propagation direction of the x-ray light. The motion induces sidebands to the response of the absorber, which we scan across the spectrum of the unknown target to gain spectral information. The oscillation further introduces a dependence of the detected light on the motional phase at the time of x-ray excitation as an additional controllable degree of freedom. We show how a Fourier analysis with respect to this phase enables one to selectively extract parts of the recorded intensity after the actual experiment, throughout the data analysis. This allows one to improve the spectral recovery by removing unwanted signal contributions. Our method is capable of gaining spectral information from the entire measured intensity, and not only from the intensity at late times after the excitation, such that a significantly higher part of the signal photons can be used. Furthermore, it not only enables one to measure the amplitude of the spectral response but also its phase.

Recent experiments have reported evidence of dominant electron-hole scattering in the electric conductivity of suspended bilayer graphene near charge neutrality. According to these experiments, plots of the electric conductivity as a function of $\mu /k_{B}T$ (chemical potential scaled with temperature) obtained for different temperatures in the range of $12\mathrm{K}\lesssim T\lesssim 40\mathrm{K}$ collapse on a single curve independent of $T$. In a recent theory, this observation has been taken as an indication that the main subdominant scattering process is not electron impurity but electron-phonon. Here, we demonstrate that the collapse of the data on a single curve can be explained without invoking electron-phonon scattering but assuming that the suspended bilayer graphene is not a truly gapless system and by including the effect of electron-hole puddles in the subdominant charged impurity scattering mechanism. With a gap of $\sim 5\mathrm{meV}$, our theory produces excellent agreement with the observed conductivity over the full reported range of temperatures. These results are based on the hydrodynamic theory of conductivity, which, thus, emerges as a solid foundation for the analysis of experiments and the estimation of the band gap in multiband systems.

Correlations in topological states of matter provide a rich phenomenology, including a reduction in the topological classification of the interacting system compared to its noninteracting counterpart. This happens when two phases that are topologically distinct on the noninteracting level become adiabatically connected once interactions are included. Here, we use a numerically exact quantum Monte Carlo method to study such a topological reduction. We consider a two-dimensional charge-conserving analog of the Levin-Gu superconductor whose classification is reduced from $\mathbb{Z}$ to ${\mathbb{Z}}_4$. We may expect any symmetry-preserving interaction that leads to a symmetric gapped ground state at strong coupling, and consequently a gapped symmetric surface, to be sufficient for such reduction. Here, we provide a counterexample by considering an interaction that (i) leads to a symmetric gapped ground state at sufficient strength, and (ii) does not allow for any adiabatic path connecting the trivial phase to the topological phase with $w=4$. The latter statement is established by numerically mapping the phase diagram as a function of the interaction strength and a parameter tuning the topological invariant. Instead of the adiabatic connection, the system exhibits an extended region of spontaneous symmetry breaking separating the topological sectors. Upon the inclusion of frustration, the size of this long-range-ordered region is reduced until it gives way to a first-order phase transition. Within the investigated range of parameters, there is no adiabatic path deforming the formerly distinct free-fermion states into each other. We conclude that an interaction that trivializes the surface of a gapped topological phase is a necessary but not sufficient condition to establish an adiabatic path within the interaction-reduced classification. In other words, the class of interactions that trivializes the surface is different (likely larger) from the class of interactions that establishes an adiabatic connection in the bulk.

High-temperature superconductors are strongly coupled systems which present a complicated phase diagram with many coexisting phases. This makes it difficult to understand the mechanism which generates their singular transport properties. Hydrodynamics, which mostly relies on the symmetries of the system without referring to any specific microscopic mechanism, constitutes a promising framework to analyze these materials. In this paper we show that, in the strange metal phase of the cuprates, a whole set of transport coefficients are described by a universal hydrodynamic framework once one accounts for the effects of quantum critical charge-density waves. We corroborate our theoretical prediction by measuring the DC transport properties of Bi-2201 close to optimal doping, proving the validity of our approach. Our argument can be used as a consistency check to understand the universality class governing the behavior of high-temperature cuprate superconductors.

We directly compare the mean-field and the many-body approaches, in a one-dimensional Bose system in a harmonic trap. Both contact and dipolar interactions are considered. We obtain eigenstates of the many-body system by exact diagonalization with a truncated basis. We propose a multiatom version of the phase-imprinting method to generate dark solitons in the system. We begin with a general analysis of system dynamics and observe the emergence of a dark soliton and a shock wave in the form of sloshing motion of the condensate upon phase imprinting. The center of mass and soliton go out of phase because the soliton does not oscillate with the trap frequency. A detailed investigation of frequencies reveals significant differences in the results obtained in the mean-field versus the many-body picture.

The full exploitation of non-Abelian symmetries in tensor network states (TNSs) derived from a given lattice Hamiltonian is attractive in various aspects. From a theoretical perspective, it can offer deep insights into the entanglement structure and quantum information content of strongly correlated quantum many-body states. From a practical perspective, it allows one to push numerical efficiency by orders of magnitude. Physical expectation values based on TNSs require the full contraction of a given tensor network, with the elementary ingredient being a pairwise contraction. While well established for no or just Abelian symmetries, this can become quickly extremely involved and cumbersome for general non-Abelian symmetries. As shown in this paper, however, the elementary step of a pairwise contraction of tensors of arbitrary rank can be tackled in a transparent and efficient manner by introducing so-called X-symbols. These deal with the pairwise contraction of the generalized underlying Clebsch-Gordan tensors (CGTs). They can be computed deterministically once and for all, and hence they can also be tabulated. Akin to $6j$-symbols, X-symbols are generally much smaller than their constituting CGTs. In applications, they solely affect the tensors of reduced matrix elements and therefore, once tabulated, allow one to completely sidestep the explicit usage of CGTs, and thus to greatly increase numerical efficiency.

A comprehensive theory of superconductivity in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ must simultaneously explain experiments that suggest even-parity superconducting order and yet others that have suggested broken time-reversal symmetry. Completeness further requires that the theory is applicable to isoelectronic ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$, a Mott-Hubbard semiconductor that exhibits an unprecedented insulator-to-metal transition which can be driven by very small electric field or current, and also by doping with very small concentration of electrons, leading to a metallic state proximate to ferromagnetism. A valence transition model, previously proposed for superconducting cuprates [Mazumdar, Phys. Rev. B 98, 205153 (2018)], is here extended to ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ and ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$. The insulator-to-metal transition is distinct from that expected from the simple melting of the Mott-Hubbard semiconductor. Rather, the Ru ions occur as low spin ${\mathrm{Ru}}^{4+}$ in the semiconductor, and as high spin ${\mathrm{Ru}}^{3+}$ in the metal, the driving force behind the valence transition being the strong spin-charge coupling and consequent large ionization energy in the low charge state. Metallic and superconducting ruthenates are thus two-component systems in which the half-filled high spin ${\mathrm{Ru}}^{3+}$ ions determine the magnetic behavior but not transport, while the charge carriers are entirely on the layer oxygen ions, which have an average charge of $-1.5$. Spin-singlet superconductivity in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ evolves from the correlated lattice-frustrated $\frac{3}{4}$-filled band of layer oxygen ions alone, in agreement with quantum many-body calculations that have demonstrated enhancement by electron-electron interactions of superconducting pair-pair correlations uniquely at or very close to this filling [Gomes, Wasanthi De Silva, Dutta, Clay, and Mazumdar, Phys. Rev. B 93, 165110 (2016); Wasanthi De Silva, Gomes, Mazumdar, and Clay, Phys. Rev. B 93, 205111 (2016)]. Several model-specific experimental predictions are made, including that spin susceptibility due to Ru ions will remain unchanged as ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ is taken through superconducting $T_c$.

In systems with overdamped dynamics, the Lorentz force reduces the diffusivity of a Brownian particle in the plane perpendicular to the magnetic field. The anisotropy in diffusion implies that the Fokker-Planck equation for the probability distribution of the particle acquires a tensorial coefficient. The tensor, however, is not a typical diffusion tensor due to the antisymmetric elements, which account for the fact that Lorentz force curves the trajectory of a moving charged particle. This gives rise to unusual dynamics with features such as additional Lorentz fluxes and a nontrivial density distribution, unlike a diffusive system. The equilibrium properties are, however, unaffected by the Lorentz force. Here we show that by stochastically resetting the Brownian particle, a nonequilibrium steady state can be created that preserves the hallmark features of dynamics under Lorentz force. We then consider a minimalistic example of a spatially inhomogeneous magnetic field, which shows how Lorentz fluxes fundamentally alter the boundary conditions giving rise to an unusual stationary state.

Theories of symmetry-based indicators and topological quantum chemistry, while powerful in diagnosing gapped topological materials, cannot be directly applied to diagnosing band degeneracies at/between high-symmetry momenta due to the violation of the compatibility conditions. However, the only information that compatibility condition can tell us is whether there are band degeneracies at/between high-symmetry momenta or not. Here we design a recursive protocol that utilizes indicators of maximal subgroups to infer the topological information of band degeneracies crossing high-symmetry lines without implementing a heavy numerical calculation, such as the existence, type, number, configuration for the band degeneracies, and so on. For demonstration, the method is used to predict the existence of ideal Weyl phonons in ${\mathrm{In}}_2\mathrm{Te}$ and node-cage phonons in ZrSiO, respectively.

In topological systems, a modulation in the gap onset near interfaces can lead to the appearance of massive edge states, as were first described by Volkov and Pankratov. In this work, we study graphene nanoribbons in the presence of intrinsic spin-orbit coupling smoothly modulated near the system edges. We show that this space modulation leads to the appearance of Volkov-Pankratov states, in addition to the topologically protected ones. We obtain this result by means of two complementary methods, one based on the effective low-energy Dirac equation description and the other on a fully numerical tight-binding approach, finding excellent agreement between the two. We then show how transport measurements might reveal the presence of Volkov-Pankratov states, and discuss possible graphenelike structures in which such states might be observed.

Quantum materials that host a flatband, such as pseudospin-1 lattices and magic-angle twisted bilayer graphene, can exhibit drastically new physical phenomena including unconventional superconductivity, orbital ferromagnetism, and Chern insulating behaviors. We report a surprising class of electronic in-gap edge states in pseudospin-1 materials without the conventional need of band-inversion topological phase transitions or introducing magnetism via an external magnetic type of interactions. In particular, we find that, in two-dimensional gapped (insulating) Dirac systems of massive spin-1 quasiparticles, in-gap edge modes can emerge through only an electrostatic potential applied to a finite domain. Associated with these unconventional edge modes are spontaneous formation of pronounced domain-wall spin textures, which exhibit the feature of out-of-plane spin-angular momentum locking on both sides of the domain boundary and are quite robust against boundary deformations and impurities despite a lack of an explicit topological origin. The in-gap modes are formally three-component evanescent wave solutions, akin to the Jackiw-Rebbi type of bound states. Such modes belong to a distinct class due to the following physical reasons: three-component spinor wave function, unusual boundary conditions, and a shifted flatband induced by the external scalar potential. Not only is the finding of fundamental importance, but it also paves the way for generating highly controllable in-gap edge states with emergent spin textures using the traditional semiconductor gate technology. Results are validated using analytic calculations of a continuum Dirac-Weyl model and tight-binding simulations of realistic materials through characterizations of local density of state spectra and resonant tunneling conductance.

Shear viscosity is an important characterization of how a many-body system behaves like a fluid. Here we study the shear viscosity of a strongly interacting solvable model in two spatial dimensions, consisting of coupled Sachdev-Ye-Kitaev (SYK) islands. As the temperature is lowered, the model exhibits a crossover from an incoherent metal with local criticality to a marginal Fermi liquid. We find that while the shear viscosity to entropy density ratio satisfies the Kovtun-Son-Starinets (KSS) bound in the marginal Fermi liquid regime, it can strongly violate the KSS bound within a finite and robust temperature range in the incoherent metal regime, implying nearly perfect fluidity of the incoherent metal with local criticality. To the best of our knowledge, it provides the first translationally invariant example violating the KSS bound with known gauge-gravity correspondence.

Four-dimensional quantum Hall (QH) models usually rely on synthetic dimensions for their simulation in experiment. Here, we study a QH system which features a nontrivial configuration of three-dimensional Weyl cones on its boundaries. We propose a three-dimensional analog of this model in the form of a dissipative Weyl semimetal (WSM) described by a non-Hermitian (NH) Hamiltonian, which in the long-time limit manifests the anomalous boundary physics of the four-dimensional QH model in the bulk spectrum. The topology of the NH WSM is captured by a three-dimensional winding number whose value is directly related to the total chirality of the surviving Weyl nodes. Upon taking open boundary conditions, instead of Fermi arcs, we find exceptional points with an order that scales with system size.

Recent proposals for spin-1 Kitaev materials, such as honeycomb Ni oxides with heavy elements of Bi and Sb, have shown that these compounds naturally give rise to antiferromagnetic (AFM) Kitaev couplings. Conceptual interest in such AFM Kitaev systems has been sparked by the observation of a transition to a gapless $U\left(1\right)$ spin liquid at intermediate field strengths in the AFM spin-1/2 Kitaev model. However, all hitherto known spin-1/2 Kitaev materials exhibit ferromagnetic bond-directional exchanges. Here we discuss the physics of the spin-1 Kitaev model in a magnetic field and show, by extensive numerical analysis, that for AFM couplings it exhibits an extended gapless quantum spin liquid at intermediate field strengths. The close analogy to its spin-1/2 counterpart suggests that this gapless spin liquid is a $U\left(1\right)$ spin liquid with a neutral Fermi surface that gives rise to enhanced thermal transport signatures.

Since its discovery, iron-based superconductivity has been known to develop near an antiferromagnetic order, but this paradigm fails in the iron chalcogenide FeSe, whose single-layer version holds the record for the highest superconducting transition temperature in the iron-based superconductors. The striking puzzle that FeSe displays nematic order (spontaneously broken lattice rotational symmetry) while being nonmagnetic, has led to several competing proposals for its origin in terms of either the $3d$-electron's orbital degrees of freedom or spin physics in the form of frustrated magnetism. Here we argue that the phase diagram of FeSe under pressure could be qualitatively described by a quantum spin model with highly frustrated interactions. We implement both the site-factorized wave-function analysis and the large-scale density matrix renormalization group (DMRG) in cylinders to study the spin-1 bilinear-biquadratic model on the square lattice, and identify quantum transitions from the well-known $(\pi ,0)$ antiferromagnetic state to an exotic $(\pi ,0)$ antiferroquadrupolar order, either directly or through a $(\pi /2,\pi )$ antiferromagnetic state. These many phases, while distinct, are all nematic. We also discuss our theoretical ground-state phase diagram for the understanding of the experimental low-temperature phase diagram obtained by the NMR [Wang et al., Phys. Rev. Lett. 117, 237001 (2016)] and x-ray scattering [Kothapalli et al., Nat. Commun. 7, 12728 (2016)] measurements in pressurized FeSe. Our results suggest that superconductivity in a wide range of iron-based materials has a common origin in the antiferromagnetic correlations of strongly correlated electrons.

Inspired by recent developments generalizing Jordan-Wigner dualities to higher dimensions [Ann. Phys. 393, 234 (2018)], we develop a framework of such dualities using an algebraic formalism for translation-invariant Hamiltonians proposed by Haah [Commun. Math. Phys. 324, 351 (2013)]. We prove that given a translation-invariant fermionic system with general $q$-body interactions, where $q$ is even, a local mapping preserving global fermion parity to a dual Pauli spin model exists and is unique up to a choice of basis. Furthermore, the dual spin model is constructive, and we present various examples of these dualities. As an application, we bosonize fermionic systems where free-fermion hopping terms are absent $(q\ge 4)$ and fermion parity is conserved on submanifolds such as higher-form, line, planar or fractal symmetry. For some cases in 3+1D, bosonizing such a system can give rise to fracton models where the emergent particles are immobile but yet can behave in certain ways like fermions. These models may be examples of new nonrelativistic 't Hooft anomalies. Furthermore, fermionic subsystem symmetries are also present in various Majorana stabilizer codes, such as the color code or the checkerboard model, and we give examples where their duals are cluster states or new fracton models distinct from their doubled CSS codes.

Bose-Einstein condensates of exciton-polaritons are known for their fascinating coherent and polarization properties. The spin state of the condensate is reflected in polarization of the exciton-polariton emission, with temporal fluctuations of this polarization being, in general, capable of reflecting quantum statistics of polaritons in the condensate. To study the polarization properties of optically trapped polariton condensates, we take advantage of the spin noise spectroscopy technique. The ratio between the noise of ellipticity of the condensate emission and its polarization plane rotation noise is found to be dependent, in a nontrivial way, on the intensity of continuous wave nonresonant laser pumping. We show that the interplay between the ellipticity and the rotation noise can be explained in terms of the competition between the self-induced Larmor precession of the condensate pseudospin and the static polarization anisotropy of the microcavity.

A core technology that has emerged from the artificial intelligence revolution is the recurrent neural network (RNN). Its unique sequence-based architecture provides a tractable likelihood estimate with stable training paradigms, a combination that has precipitated many spectacular advances in natural language processing and neural machine translation. This architecture also makes a good candidate for a variational wave function, where the RNN parameters are tuned to learn the approximate ground state of a quantum Hamiltonian. In this paper, we demonstrate the ability of RNNs to represent several many-body wave functions, optimizing the variational parameters using a stochastic approach. Among other attractive features of these variational wave functions, their autoregressive nature allows for the efficient calculation of physical estimators by providing independent samples. We demonstrate the effectiveness of RNN wave functions by calculating ground-state energies, correlation functions, and entanglement entropies for several quantum spin models of interest to condensed-matter physicists in one and two spatial dimensions.