We study a topological phase of interacting bosons in ($3+1$) dimensions that is protected by charge conservation and time-reversal symmetry. We present an explicit lattice model that realizes this phase and that can be studied in sign-free Monte Carlo simulations. The idea behind our model is to bind bosons to topological defects called hedgehogs. We determine the phase diagram of the model and identify a phase where such bound states are proliferated. In this phase, we observe a Witten effect in the bulk whereby an external monopole binds half of the elementary boson charge, which confirms that it is a bosonic topological insulator. We also study the boundary between the topological insulator and a trivial insulator. We find a surface phase diagram that includes exotic superfluids, a topologically ordered phase, and a phase with a Hall effect quantized to one-half of the value possible in a purely two-dimensional system. We also present models that realize symmetry-enriched topologically ordered phases by binding multiple hedgehogs to each boson; these phases show charge fractionalization and intrinsic topological order as well as a fractional Witten effect.

We present detailed measurements of the temperature-dependent Raman spectra of optimally doped ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{Fe}}_2{\mathrm{As}}_2$ and analyze the low-temperature spectra based on local-density-approximation band-structure calculations and the subsequent estimation of effective Raman vertices. Experimentally, a narrow, emergent mode appears in the $B_{1g}$ ($d_{x^2-y^2}$) Raman spectra only below $T_c$, well into the superconducting state and at an energy below twice the energy gap on the electron Fermi-surface sheets. The Raman spectra can be reproduced quantitatively with estimates for the magnitude and momentum-space structure of an $A_{1g}$ ($s$-wave) pairing gap on different Fermi-surface sheets, as well as the identification of the emergent sharp feature as a Bardasis-Schrieffer exciton. Formed as a Cooper-pair bound state in a subdominant $d_{x^2-y^2}$ channel, the binding energy of the exciton relative to the gap edge shows that the coupling strength in the subdominant channel is as strong as 60% of that in the dominant $s$-wave channel. This result suggests that $d_{x^2-y^2}$ may be the dominant pairing symmetry in Fe-based superconductors that lack central hole bands.

We report magnetotransport studies on a gated strained HgTe device. This material is a three-dimensional topological insulator and exclusively shows surface-state transport. Remarkably, the Landau-level dispersion and the accuracy of the Hall quantization remain unchanged over a wide density range ($3\times {10}^{11}{\mathrm{cm}}^{-2}<n<2\times {10}^{12}{\mathrm{cm}}^{-2}$). These observations imply that even at large carrier densities, the transport is surface-state dominated, where bulk transport would have been expected to coexist already. Moreover, the density dependence of the Dirac-type quantum Hall effect allows us to identify the contributions from the individual surfaces. A $k·p$ model can describe the experiments but only when assuming a steep band bending across the regions where the topological surface states are contained. This steep potential originates from the specific screening properties of Dirac systems and causes the gate voltage to influence the position of the Dirac points rather than that of the Fermi level.

While the topological order in two dimensions has been studied extensively since the discovery of the integer and fractional quantum Hall systems, topological states in three spatial dimensions are much less understood. In this paper, we propose a general formalism for constructing a large class of three-dimensional topological states by stacking layers of 2D topological states and introducing coupling between them. Using this construction, different types of topological states can be obtained, including those with only surface topological order and no bulk topological quasiparticles, and those with topological order both in the bulk and at the surface. For both classes of states, we study its generic properties and present several explicit examples. As an interesting consequence of this construction, we obtain example systems with nontrivial braiding statistics between string excitations. In addition to studying the string-string braiding in the example system, we propose a topological field-theory description for the layer-constructed systems, which captures not only the string-particle braiding statistics but also the string-string braiding statistics when the coupling is twisted. Last, we provide a proof of a general identity for Abelian string statistics and discuss an example system with non-Abelian strings.

Protecting quantum information from decoherence due to environmental noise is vital for fault-tolerant quantum computation. To this end, standard quantum error correction employs parallel projective measurements of individual particles, which makes the system extremely complicated. Here, we propose measurement-free topological protection in two dimensions without any selective addressing of individual particles. We make use of engineered dissipative dynamics and feedback operations to reduce the entropy generated by decoherence in such a way that quantum information is topologically protected. We calculate an error threshold, below which quantum information is protected, without assuming selective addressing, projective measurements, or instantaneous classical processing. All physical operations are local and translationally invariant, and no parallel projective measurement is required, which implies high scalability. Furthermore, since the engineered dissipative dynamics we utilize has been well studied in quantum simulation, the proposed scheme can be a promising route progressing from quantum simulation to fault-tolerant quantum information processing.

Quantum spin-ice represents a paradigmatic example of how the physics of frustrated magnets is related to gauge theories. In the present work, we address the problem of approximately realizing quantum spin ice in two dimensions with cold atoms in optical lattices. The relevant interactions are obtained by weakly laser-admixing Rydberg states to the atomic ground-states, exploiting the strong angular dependence of van der Waals interactions between Rydberg $p$ states together with the possibility of designing steplike potentials. This allows us to implement Abelian gauge theories in a series of geometries, which could be demonstrated within state-of-the-art atomic Rydberg experiments. We numerically analyze the family of resulting microscopic Hamiltonians and find that they exhibit both classical and quantum order by disorder, the latter yielding a quantum plaquette valence bond solid. We also present strategies to implement Abelian gauge theories using both $s$- and $p$-Rydberg states in exotic geometries, e.g., on a 4–8 lattice.

The idea of topological quantum computation is to build powerful and robust quantum computers with certain macroscopic quantum states of matter called topologically ordered states. These systems have degenerate ground states that can be used as robust “topological qubits” to store and process quantum information. In this paper, we propose a new experimental setup that can realize topological qubits in a simple bilayer fractional quantum Hall system with proper electric gate configurations. Our proposal is accessible with current experimental techniques, involves well-established topological states, and, moreover, can realize a large class of topological qubits, generalizing the Majorana zero modes studied in recent literature to more computationally powerful possibilities. We propose three tunneling and interferometry experiments to detect the existence and nonlocal topological properties of the topological qubits.

We report point-contact measurements of anisotropic magnetoresistance (AMR) in a single crystal of antiferromagnetic Mott insulator ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. The point-contact technique is used here as a local probe of magnetotransport properties on the nanoscale. The measurements at liquid nitrogen temperature reveal negative magnetoresistances (up to 28%) for modest magnetic fields (250 mT) applied within the ${\mathrm{IrO}}_2$ $a\text{−}b$ plane and electric currents flowing perpendicular to the plane. The angular dependence of magnetoresistance shows a crossover from fourfold to twofold symmetry in response to an increasing magnetic field with angular variations in resistance from 1% to 14%. We tentatively attribute the fourfold symmetry to the crystalline component of AMR and the field-induced transition to the effects of applied field on the canting of antiferromagnetic-coupled moments in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. The observed AMR is very large compared to the crystalline AMRs in $3d$ transition metal alloys or oxides (0.1%–0.5%) and can be associated with the large spin-orbit interactions in this $5d$ oxide while the transition provides evidence of correlations between electronic transport, magnetic order, and orbital states. The finding of this work opens an entirely new avenue to not only gain a new insight into physics associated with spin-orbit coupling but also to better harness the power of spintronics in a more technically favorable fashion.

A single crystal of isovalently substituted $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Ru}}_x{)}_2{\mathrm{As}}_2$ ($x=0.24$) is sequentially irradiated with 2.5 MeV electrons up to a maximum dose of $2.1\times 10^{19}$ $e^{-}/{\mathrm{cm}}^2$. The electrical resistivity is measured in situ at $T=22\mathrm{K}$ during the irradiation and ex situ as a function of temperature between subsequent irradiation runs. Upon irradiation, the superconducting transition temperature $T_c$ decreases and the residual resistivity ${\rho }_0$ increases. We find that electron irradiation leads to the fastest suppression of $T_c$ compared to other types of artificially introduced disorder, probably due to the strong short-range potential of the pointlike irradiation defects. A more detailed analysis within a multiband scenario with variable scattering potential strength shows that the observed $T_c$ versus ${\rho }_0$ is fully compatible with $s_{\pm }$ pairing, in contrast to earlier claims that this model leads to a too rapid suppression of $T_c$ with scattering.

The phenomenon of ultrastrong light-matter interaction of a two-dimensional electron gas within a lumped element electronic circuit resonator is explored. The gas is coupled through the oscillating electric field of the capacitor, and in the limit of very small capacitor volumes, the total number of electrons of the system can be reduced to only a few. One of the peculiar features of our quantum mechanical system is that its Hamiltonian evolves from the fermionic Rabi model to the bosonic Hopfield model for light-matter coupling as the number of electrons is increased. We show that the Dicke states, introduced to describe the atomic super-radiance, are the natural base to describe the crossover between the two models. Furthermore, we illustrate how the ultrastrong coupling regime in the system and the associated antiresonant terms of the quantum Hamiltonian have a fundamentally different impact in the fermionic and bosonic cases. In the intermediate regime, our system behaves like a multilevel quantum bit with nonharmonic energy spacing, owing to the particle-particle interactions. Such a system can be inserted into a technological semiconductor platform, thus opening interesting perspectives for electronic devices where the readout of quantum electrodynamical properties is obtained via the measure of a DC current.

In some many-body systems, certain ground-state entanglement (Rényi) entropies increase even as the correlation length decreases. This entanglement nonmonotonicity is a potential indicator of nonclassicality. In this work, we demonstrate that such a phenomenon, known as lack of local convertibility, is due to the edge-state (de)construction occurring in the system. To this end, we employ the example of the Ising chain, displaying an order-disorder quantum phase transition. Employing both analytical and numerical methods, we compute entanglement entropies for various system bipartitions $(A|B)$ and consider ground states with and without Majorana edge states. We find that the thermal ground states, enjoying the Hamiltonian symmetries, show lack of local convertibility if either $A$ or $B$ is smaller than, or of the order of, the correlation length. In contrast, the ordered (symmetry-breaking) ground state is always locally convertible. The edge-state behavior explains all these results and could disclose a paradigm to understand local convertibility in other quantum phases of matter. The connection we establish between convertibility and nonlocal, quantum correlations provides a clear criterion of which features a universal quantum simulator should possess to outperform a classical machine.

We discuss how to formulate lattice gauge theories in the tensor-network language. In this way, we obtain both a consistent-truncation scheme of the Kogut-Susskind lattice gauge theories and a tensor-network variational ansatz for gauge-invariant states that can be used in actual numerical computations. Our construction is also applied to the simplest realization of the quantum link models or gauge magnets and provides a clear way to understand their microscopic relation with the Kogut-Susskind lattice gauge theories. We also introduce a new set of gauge-invariant operators that modify continuously Rokhsar-Kivelson wave functions and can be used to extend the phase diagrams of known models. As an example, we characterize the transition between the deconfined phase of the $Z_2$ lattice gauge theory and the Rokhsar-Kivelson point of the $U(1)$ gauge magnet in 2D in terms of entanglement entropy. The topological entropy serves as an order parameter for the transition but not the Schmidt gap.

We report temperature-dependent measurements of longitudinal spin Seebeck effects (LSSEs) in $\mathrm{Pt}/{\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ $(\mathrm{YIG})/\mathrm{Pt}$ systems in a high temperature range from room temperature to above the Curie temperature of YIG. The experimental results show that the magnitude of the LSSE voltage in the $\mathrm{Pt}/\mathrm{YIG}/\mathrm{Pt}$ systems rapidly decreases with increasing the temperature and disappears above the Curie temperature. The critical exponent of the LSSE voltage in the $\mathrm{Pt}/\mathrm{YIG}/\mathrm{Pt}$ systems at the Curie temperature is estimated to be 3, which is much greater than that for the magnetization curve of YIG. This difference highlights the fact that the mechanism of the LSSE cannot be explained in terms of simple static magnetic properties in YIG.

Topological insulators (TIs) have attracted immense interest because they host helical surface states. Protected by time-reversal symmetry, they are robust to nonmagnetic disorder. When superconductivity is induced in these helical states, they are predicted to emulate $p$-wave pairing symmetry, with Majorana states bound to vortices. Majorana bound states possess non-Abelian exchange statistics that can be probed through interferometry. Here, we take a significant step towards Majorana interferometry by observing pronounced Fabry-Pérot oscillations in a TI sandwiched between a superconducting and a normal lead. For energies below the superconducting gap, we observe a doubling in the frequency of the oscillations, arising from an additional phase from Andreev reflection. When a magnetic field is applied perpendicular to the TI surface, a number of very sharp and gate-tunable conductance peaks appear at or near zero energy, which has consequences for interpreting spectroscopic probes of Majorana fermions. Our results demonstrate that TIs are a promising platform for exploring phase-coherent transport in a solid-state system.

Many-body localization, the persistence against electron-electron interactions of the localization of states with nonzero excitation energy density, poses a challenge to current methods of theoretical and numerical analyses. Numerical simulations have so far been limited to a small number of sites, making it difficult to obtain reliable statements about the thermodynamic limit. In this paper, we explore the ways in which a relatively small quantum computer could be leveraged to study many-body localization. We show that, in addition to studying time evolution, a quantum computer can, in polynomial time, obtain eigenstates at arbitrary energies to sufficient accuracy that localization can be observed. The limitations of quantum measurement, which preclude the possibility of directly obtaining the entanglement entropy, make it difficult to apply some of the definitions of many-body localization used in the recent literature. We discuss alternative tests of localization that can be implemented on a quantum computer.

We perform systematic investigations of transport through graphene on hexagonal boron nitride (hBN) substrates, together with confocal Raman measurements and a targeted theoretical analysis, to identify the dominant source of disorder in this system. Low-temperature transport measurements on many devices reveal a clear correlation between the carrier mobility $\mu$ and the width $n^{*}$ of the resistance peak around charge neutrality, demonstrating that charge scattering and density inhomogeneities originate from the same microscopic mechanism. The study of weak localization unambiguously shows that this mechanism is associated with a long-ranged disorder potential and provides clear indications that random pseudomagnetic fields due to strain are the dominant scattering source. Spatially resolved Raman spectroscopy measurements confirm the role of local strain fluctuations, since the linewidth of the Raman 2D peak—containing information of local strain fluctuations present in graphene—correlates with the value of maximum observed mobility. The importance of strain is corroborated by a theoretical analysis of the relation between $\mu$ and $n^{*}$ that shows how local strain fluctuations reproduce the experimental data at a quantitative level, with $n^{*}$ being determined by the scalar deformation potential and $\mu$ by the random pseudomagnetic field (consistently with the conclusion drawn from the analysis of weak localization). Throughout our study, we compare the behavior of devices on hBN substrates to that of devices on ${\mathrm{SiO}}_2$ and ${\mathrm{SrTiO}}_3$, and find that all conclusions drawn for the case of hBN are compatible with the observations made on these other materials. These observations suggest that random strain fluctuations are the dominant source of disorder for high-quality graphene on many different substrates, and not only on hexagonal boron nitride.

The nature of ordering in dilute dipolar interacting systems dates back to the work of Debye and is one of the most basic, oldest and as-of-yet unsettled problems in magnetism. While spin-glass order is readily observed in several RKKY-interacting systems, dipolar spin glasses are the subject of controversy and ongoing scrutiny, e.g., in ${\mathrm{LiHo}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$, a rare-earth randomly diluted uniaxial (Ising) dipolar system. In particular, it is unclear if the spin-glass phase in these paradigmatic materials persists in the limit of zero concentration or not. We study an effective model of ${\mathrm{LiHo}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$ using large-scale Monte Carlo simulations that combine parallel tempering with a special cluster algorithm tailored to overcome the numerical difficulties that occur at extreme dilutions. We find a paramagnetic to spin-glass phase transition for all ${\mathrm{Ho}}^{+}$ ion concentrations down to the smallest concentration numerically accessible, 0.1%, and including ${\mathrm{Ho}}^{+}$ ion concentrations that coincide with those studied experimentally up to 16.7%. Our results suggest that randomly diluted dipolar Ising systems have a spin-glass phase in the limit of vanishing dipole concentration, with a critical temperature vanishing linearly with concentration. The agreement of our results with mean-field theory testifies to the irrelevance of fluctuations in interactions strengths, albeit being strong at small concentrations, to the nature of the low-temperature phase and the functional form of the critical temperature of dilute anisotropic dipolar systems. Deviations from linearity in experimental results at the lowest concentrations are discussed.

The quantum evolution that occurs after a metallic lead is suddenly connected to an electron system contains information about the excitation spectrum of the combined system. We exploit this type of “quantum quench” to probe the presence of Majorana fermions at the ends of a topological superconducting wire. We obtain an algebraically decaying overlap (Loschmidt echo) $\mathcal{L}(t)={|⟨\psi (0)|\psi (t)⟩|}^2\sim t^{-\alpha }$ for large times after the quench, with a universal critical exponent $\alpha =\frac{1}{4}$ that is found to be remarkably robust against details of the setup, such as interactions in the normal lead, the existence of additional lead channels, or the presence of bound levels between the lead and the superconductor. As in recent quantum-dot experiments, this exponent could be measured by optical absorption, offering a new signature of Majorana zero modes that is distinct from interferometry and tunneling spectroscopy.

Quantum phase transitions are usually studied in terms of Hermitian Hamiltonians. However, cold-atom experiments are intrinsically non-Hermitian because of spontaneous decay. Here, we show that non-Hermitian systems exhibit quantum phase transitions that are beyond the paradigm of Hermitian physics. We consider the non-Hermitian $XY$ model, which can be implemented using three-level atoms with spontaneous decay. We exactly solve the model in one dimension and show that there is a quantum phase transition from short-range order to quasi-long-range order despite the absence of a continuous symmetry in the Hamiltonian. The ordered phase has a frustrated spin pattern. The critical exponent $\nu$ can be 1 or $1/2$. Our results can be seen experimentally with trapped ions, cavity QED, and atoms in optical lattices.

We consider two-dimensional lattice models that support Ising anyonic excitations and are coupled to a thermal bath. We propose a phenomenological model for the resulting short-time dynamics that includes pair creation, hopping, braiding, and fusion of anyons. By explicitly constructing topological quantum error-correcting codes for this class of system, we use our thermalization model to estimate the lifetime of the quantum information stored in the encoded spaces. To decode and correct errors in these codes, we adapt several existing topological decoders to the non-Abelian setting. We perform large-scale numerical simulations of these two-dimensional Ising anyon systems and find that the thresholds of these models range from 13% to 25%. To our knowledge, these are the first numerical threshold estimates for quantum codes without explicit additive structure.