Topological Quantum Synchronization of Fractionalized Spins.

The gapped symmetric phase of the Affleck-Kennedy-Lieb-Tasaki model exhibits fractionalized spins at the ends of an open chain. We show that breaking SU(2) symmetry and applying a global spin-lowering dissipator achieves synchronization of these fractionalized spins. Additional local dissipators ensure convergence to the ground state manifold. In order to understand which aspects of this synchronization are robust within the entire Haldane-gap phase, we reduce the biquadratic term, which eliminates the need for an external field but destabilizes synchronization. Within the ground state subspace, stability is regained using only the global lowering dissipator. These results demonstrate that fractionalized degrees of freedom can be synchronized in extended systems with a significant degree of robustness arising from topological protection. A direct consequence is that permutation symmetries are not required for the dynamics to be synchronized, representing a clear advantage of topological synchronization compared to synchronization induced by permutation symmetries.

Spin-polarized spatially indirect excitons in a topological insulator.

The exciton, a bound state of an electron and a hole, is a fundamental quasiparticle induced by coherent light-matter interactions in semiconductors. When the electrons and holes are in distinct spatial locations, spatially indirect excitons are formed with a much longer lifetime and a higher condensation temperature. One of the ultimate frontiers in this field is to create long-lived excitonic topological quasiparticles by driving exciton states with topological properties, to simultaneously leverage both topological effects and correlation1,2. Here we reveal the existence of a transient excitonic topological surface state (TSS) in a topological insulator, Bi2Te3. By using time-, spin- and angle-resolved photoemission spectroscopy, we directly follow the formation of a long-lived exciton state as revealed by an intensity buildup below the bulk-TSS mixing point and an anomalous band renormalization of the continuously connected TSS in the momentum space. Such a state inherits the spin-polarization of the TSS and is spatially indirect along the z axis, as it couples photoinduced surface electrons and bulk holes in the same momentum range, which ultimately leads to an excitonic state of the TSS. These results establish Bi2Te3 as a possible candidate for the excitonic condensation of TSSs3 and, in general, opens up a new paradigm for exploring the momentum space emergence of other spatially indirect excitons, such as moiré and quantum well excitons4-6, and for the study of non-equilibrium many-body topological physics.

SWAP Gate between a Majorana Qubit and a Parity-Protected Superconducting Qubit.

High fidelity quantum information processing requires a combination of fast gates and long-lived quantum memories. In this Letter, we propose a hybrid architecture, where a parity-protected superconducting qubit is directly coupled to a Majorana qubit, which plays the role of a quantum memory. The superconducting qubit is based upon a π-periodic Josephson junction realized with gate-tunable semiconducting wires, where the tunneling of individual Cooper pairs is suppressed. One of the wires additionally contains four Majorana zero modes that define a qubit. We demonstrate that this enables the implementation of a SWAP gate, allowing for the transduction of quantum information between the topological and conventional qubit. This architecture combines fast gates, which can be realized with the superconducting qubit, with a topologically protected Majorana memory.

Direct geometric probe of singularities in band structure.

A quantum system's energy landscape may have points where multiple energy surfaces are degenerate and that exhibit singular geometry of the wave function manifold, with major consequences for the system's properties. Ultracold atoms in optical lattices have been used to indirectly characterize such points in the band structure. We measured the non-Abelian transformation produced by transport directly through the singularities. We accelerated atoms along a quasi-momentum trajectory that enters, turns, and then exits the singularities at linear and quadratic band-touching points of a honeycomb lattice. Measurements after transport identified the topological winding numbers of these singularities to be 1 and 2, respectively. Our work introduces a distinct method for probing singularities that enables the study of non-Dirac singularities in ultracold-atom quantum simulators.

Imaging gate-tunable Tomonaga-Luttinger liquids in 1H-MoSe2 mirror twin boundaries.

One-dimensional electron systems exhibit fundamentally different properties than higher-dimensional systems. For example, electron-electron interactions in one-dimensional electron systems have been predicted to induce Tomonaga-Luttinger liquid behaviour. Naturally occurring grain boundaries in single-layer transition metal dichalcogenides exhibit one-dimensional conducting channels that have been proposed to host Tomonaga-Luttinger liquids, but charge density wave physics has also been suggested to explain their behaviour. Clear identification of the electronic ground state of this system has been hampered by an inability to electrostatically gate such boundaries and tune their charge carrier concentration. Here we present a scanning tunnelling microscopy and spectroscopy study of gate-tunable mirror twin boundaries in single-layer 1H-MoSe2 devices. Gating enables scanning tunnelling microscopy and spectroscopy for different mirror twin boundary electron densities, thus allowing precise characterization of electron-electron interaction effects. Visualization of the resulting mirror twin boundary electronic structure allows unambiguous identification of collective density wave excitations having two velocities, in quantitative agreement with the spin-charge separation predicted by finite-length Tomonaga-Luttinger liquid theory.

Neural Network Representation of Tensor Network and Chiral States.

We study the representational power of Boltzmann machines (a type of neural network) in quantum many-body systems. We prove that any (local) tensor network state has a (local) neural network representation. The construction is almost optimal in the sense that the number of parameters in the neural network representation is almost linear in the number of nonzero parameters in the tensor network representation. Despite the difficulty of representing (gapped) chiral topological states with local tensor networks, we construct a quasilocal neural network representation for a chiral p-wave superconductor. These results demonstrate the power of Boltzmann machines.

Four-Spin Terms and the Origin of the Chiral Spin Liquid in Mott Insulators on the Triangular Lattice.

At strong repulsion, the triangular-lattice Hubbard model is described by s=1/2 spins with nearest-neighbor antiferromagnetic Heisenberg interactions and exhibits conventional 120° order. Using the infinite density matrix renormalization group and exact diagonalization, we study the effect of the additional four-spin interactions naturally generated from the underlying Mott-insulator physics of electrons as the repulsion decreases. Although these interactions have historically been connected with a gapless ground state with emergent spinon Fermi surface, we find that, at physically relevant parameters, they stabilize a chiral spin liquid (CSL) of Kalmeyer-Laughlin (KL) type, clarifying observations in recent studies of the Hubbard model. We then present a self-consistent solution based on a mean-field rewriting of the interaction to obtain a Hamiltonian with similarities to the parent Hamiltonian of the KL state, providing a physical understanding for the origin of the CSL.

Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet.

The stranglehold of low temperatures on fascinating quantum phenomena in one-dimensional quantum magnets has been challenged recently by the discovery of anomalous spin transport at high temperatures. Whereas both regimes have been investigated separately, no study has attempted to reconcile them. For instance, the paradigmatic quantum Heisenberg spin-1/2 chain falls at low temperature within the Tomonaga-Luttinger liquid framework, while its high-temperature dynamics is superdiffusive and relates to the Kardar-Parisi-Zhang universality class in 1+1 dimensions. This Letter aims at reconciling the two regimes. Building on large-scale matrix product state simulations, we find that they are connected by a temperature-dependent spatiotemporal crossover. As the temperature T is reduced, we show that the onset of superdiffusion takes place at longer length and timescales ∝1/T. This prediction has direct consequences for experiments including nuclear magnetic resonance: it is consistent with earlier measurements on the nearly ideal Heisenberg S=1/2 chain compound Sr_{2}CuO_{3}, yet calls for new and dedicated experiments.

Realizing Hopf Insulators in Dipolar Spin Systems.

The Hopf insulator is a weak topological insulator characterized by an insulating bulk with conducting edge states protected by an integer-valued linking number invariant. The state exists in three-dimensional two-band models. We demonstrate that the Hopf insulator can be naturally realized in lattices of dipolar-interacting spins, where spin exchange plays the role of particle hopping. The long-ranged, anisotropic nature of the dipole-dipole interactions allows for the precise detail required in the momentum-space structure, while different spin orientations ensure the necessary structure of the complex phases of the hoppings. Our model features robust gapless edge states at both smooth edges, as well as sharp edges obeying a certain crystalline symmetry, despite the breakdown of the two-band picture at the latter. In an accompanying paper [T. Schuster et al., Phys. Rev. A 103, AW11986 (2021)PLRAAN2469-9926] we provide a specific experimental blueprint for implementing our proposal using ultracold polar molecules of ^{40}K^{87}Rb.

Enhanced Coherence in Superconducting Circuits via Band Engineering.

In superconducting circuits interrupted by Josephson junctions, the dependence of the energy spectrum on offset charges on different islands is 2e periodic through the Aharonov-Casher effect and resembles a crystal band structure that reflects the symmetries of the Josephson potential. We show that higher-harmonic Josephson elements described by a cos(2φ) energy-phase relation provide an increased freedom to tailor the shape of the Josephson potential and design spectra featuring multiplets of flat bands and Dirac points in the charge Brillouin zone. Flat bands provide noise-insensitive energy levels, and consequently, engineering band pairs with flat spectral gaps can help improve the coherence of the system. We discuss a modified version of a flux qubit that achieves, in principle, no decoherence from charge noise and introduce a flux qutrit that shows a spin-1 Dirac spectrum and is simultaneously quite robust to both charge and flux noise.

Intrinsic Anomalous Hall Conductivity in a Nonuniform Electric Field.

We study how the intrinsic anomalous Hall conductivity is modified in two-dimensional crystals with broken time-reversal symmetry due to weak inhomogeneity of the applied electric field. Focusing on a clean noninteracting two-band system without band crossings, we derive the general expression for the Hall conductivity at small finite wave vector q to order q^{2}, which governs the Hall response to the second gradient of the electric field. Using the Kubo formula, we show that the answer can be expressed through the Berry curvature, Fubini-Study quantum metric, and the rank-3 symmetric tensor which is related to the quantum geometric connection and physically corresponds to the gauge-invariant part of the third cumulant of the position operator. We further compare our results with the predictions made within the semiclassical approach. By deriving the semiclassical equations of motion, we reproduce the result obtained from the Kubo formula in some limits. We also find, however, that the conventional semiclassical description in terms of the definite position and momentum of the electron is not fully consistent because of singular terms originating from the Heisenberg uncertainty principle. We thus present a clear example of a case when the semiclassical approach inherently suffers from the uncertainty principle, implying that it should be applied to systems in nonuniform fields with extra care.

Criticality of Two-Dimensional Disordered Dirac Fermions in the Unitary Class and Universality of the Integer Quantum Hall Transition.

Two-dimensional (2D) Dirac fermions are a central paradigm of modern condensed matter physics, describing low-energy excitations in graphene, in certain classes of superconductors, and on surfaces of 3D topological insulators. At zero energy E=0, Dirac fermions with mass m are band insulators, with the Chern number jumping by unity at m=0. This observation lead Ludwig et al. [Phys. Rev. B 50, 7526 (1994)PRBMDO0163-182910.1103/PhysRevB.50.7526] to conjecture that the transition in 2D disordered Dirac fermions (DDF) and the integer quantum Hall transition (IQHT) are controlled by the same fixed point and possess the same universal critical properties. Given the far-reaching implications for the emerging field of the quantum anomalous Hall effect, modern condensed matter physics, and our general understanding of disordered critical points, it is surprising that this conjecture has never been tested numerically. Here, we report the results of extensive numerics on the phase diagram and criticality of 2D DDF in the unitary class. We find a critical line at m=0, with an energy-dependent localization length exponent. At large energies, our results for the DDF are consistent with state-of-the-art numerical results ν_{IQH}=2.56-2.62 from models of the IQHT. At E=0, however, we obtain ν_{0}=2.30-2.36 incompatible with ν_{IQH}. This result challenges conjectured relations between different models of the IQHT, and several interpretations are discussed.

Many-Body Chaos in the Sachdev-Ye-Kitaev Model.

Many-body chaos has emerged as a powerful framework for understanding thermalization in strongly interacting quantum systems. While recent analytic advances have sharpened our intuition for many-body chaos in certain large N theories, it has proven challenging to develop precise numerical tools capable of exploring this phenomenon in generic Hamiltonians. To this end, we utilize massively parallel, matrix-free Krylov subspace methods to calculate dynamical correlators in the Sachdev-Ye-Kitaev model for up to N=60 Majorana fermions. We begin by showing that numerical results for two-point correlation functions agree at high temperatures with dynamical mean field solutions, while at low temperatures finite-size corrections are quantitatively reproduced by the exactly solvable dynamics of near extremal black holes. Motivated by these results, we develop a novel finite-size rescaling procedure for analyzing the growth of out-of-time-order correlators. Our procedure accurately determines the Lyapunov exponent, λ, across a wide range in temperatures, including in the regime where λ approaches the universal bound, λ=2π/ß.

Superdiffusive transport of energy in one-dimensional metals.

Metals in one spatial dimension are described at the lowest energy scales by the Luttinger liquid theory. It is well understood that this free theory, and even interacting integrable models, can support ballistic transport of conserved quantities including energy. In contrast, realistic one-dimensional metals, even without disorder, contain integrability-breaking interactions that are expected to lead to thermalization and conventional diffusive linear response. We argue that the expansion of energy when such a nonintegrable Luttinger liquid is locally heated above its ground state shows superdiffusive behavior (i.e., spreading of energy that is intermediate between diffusion and ballistic propagation), by combining an analytical anomalous diffusion model with numerical matrix-product-state calculations on a specific perturbed spinless fermion chain. Different metals will have different scaling exponents and shapes in their energy spreading, but the superdiffusive behavior is stable and should be visible in time-resolved experiments.

Interactions Remove the Quantization of the Chiral Photocurrent at Weyl Points.

The chiral photocurrent or circular photogalvanic effect (CPGE) is a photocurrent that depends on the sense of circular polarization. In a disorder-free, noninteracting chiral Weyl semimetal, the magnitude of the effect is approximately quantized with a material-independent quantum e^{3}/h^{2} for reasons of band topology. We study the first-order corrections due to the Coulomb and Hubbatrd interactions in a continuum model of a Weyl semimetal in which known corrections from other bands are absent. We find that the inclusion of interactions generically breaks the quantization. The corrections are similar but larger in magnitude than previously studied interaction corrections to the (nontopological) linear optical conductivity of graphene, and have a potentially observable frequency dependence. We conclude that, unlike the quantum Hall effect in gapped phases or the chiral anomaly in field theories, the quantization of the CPGE in Weyl semimetals is not protected but has perturbative corrections in interaction strength.

Energy Drag in Particle-Hole Symmetric Systems as a Quantum Quench.

Two conducting quantum systems coupled only via interactions can exhibit the phenomenon of Coulomb drag, in which a current passed through one layer can pull a current along in the other. However, in systems with particle-hole symmetry-for instance, the half filled Hubbard model or graphene near the Dirac point-the Coulomb drag effect vanishes to leading order in the interaction. Its thermal analog, whereby a thermal current in one layer pulls a thermal current in the other, does not vanish and is indeed the dominant form of drag in particle-hole symmetric systems. By studying a quantum quench, we show that thermal drag, unlike charge drag, displays a non-Fermi's golden rule growth at short times due to a logarithmic scattering singularity generic to one dimension. Exploiting the integrability of the Hubbard model, we obtain the long-time limit of the quench for weak interactions. Finally, we comment on thermal drag effects in higher dimensional systems.

Floquet Hopf Insulators.

We predict the existence of a Floquet topological insulator in three-dimensional two-band systems, the Floquet Hopf insulator, which possesses two distinct topological invariants. One is the Hopf Z invariant, a linking number characterizing the (nondriven) Hopf topological insulator. The second invariant is an intrinsically Floquet Z_{2} invariant, and represents a condensed matter realization of the topology underlying the Witten anomaly in particle physics. Both invariants arise from topological defects in the system's time evolution, subject to a process in which defects at different quasienergies exchange even amounts of topological charge. Their contrasting classifications lead to a measurable physical consequence, namely, an unusual bulk-boundary correspondence where gapless edge modes are topologically protected, but may exist at either 0 or π quasienergy. Our results represent a phase of matter beyond the conventional classification of Floquet topological insulators.

Magnetoresistance Scaling Reveals Symmetries of the Strongly Correlated Dynamics in BaFe_{2}(As_{1-x}P_{x})_{2}.

The phenomenon of T-linear resistivity commonly observed in a number of strange metals has been widely seen as evidence for the breakdown of the quasiparticle picture of metals. This study shows that a recently discovered H/T scaling relationship in the magnetoresistance of the strange metal BaFe_{2}(As_{1-x}P_{x})_{2} is independent of the relative orientations of current and magnetic field. Rather, its magnitude and form depend only on the orientation of the magnetic field with respect to a single crystallographic axis: the direction perpendicular to the magnetic iron layers. This finding suggests that the magnetotransport scaling does not originate from the conventional averaging or orbital velocity of quasiparticles as they traverse a Fermi surface, but rather from dissipation arising from two-dimensional correlations.